* Sanctions relief doesn't come close to offsetting damage

* But easing tensions could reduce capital flight

* Trade may grow even under current sanctions

* Firm currency would help to bring down inflation

* Economic policy reforms could get a boost

By Andrew Torchia and Nadia Saleem

DUBAI, Nov 24 (Reuters) - Iran's currency jumped more than 3 percent against the U.S. dollar on Sunday as news of a breakthrough deal to curb Tehran's nuclear programme raised hopes that the economy would start recovering from international sanctions.

The deal provides for Iran to receive temporary, conditional access to several billion dollars of blocked funds over the next six months as diplomats try to negotiate a final agreement.

By itself, this will not come close to offsetting the tens of billions of dollars which Iran has lost over the past two years as the sanctions have slashed its oil sales and largely frozen it out of the global banking system.

But by reducing the chance of military action against Iran and raising the prospect of more sanctions relief in future, the Geneva pact may stem capital flight from the country and encourage a partial revival of domestic investment.

This could be enough to pull the economy out of the recession which has gripped it for most of the past two years, while encouraging Iranian and foreign businessmen to begin rebuilding trade ties.

"We are feeling the positive sentiment in Iran," Nariman Aflani, a foreign exchange trader at AFI Group, an Iranian civil engineering firm in Tehran, said by telephone.

Prices of construction materials such as ceramics and cement in Iran are already coming down because people hope a gradual loosening of sanctions will make it easier for the country to obtain supplies from abroad, he said.

Winners and losers of Iran economic thaw

U.S. government fact sheet on sanctions relief:

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BLOCKED BILLIONS

Under Sunday's deal in Geneva, Iran will receive potential access to $1.5 billion in revenue from trade in gold and precious metals, and permission to transfer $4.2 billion of revenue from its oil sales across borders.

In total, the concessions are worth about $7 billion - a small sum compared to the continued cost of the sanctions, which will deprive Iran of about $30 billion of oil revenues over the next six months, the U.S. government said.

But this comparison underestimates the importance of the Geneva deal to the economy of 75 million people, as the Iranian rial's jump against the dollar on Sunday underlined.

The rial traded at around 29,000 against the dollar in Tehran's free market, up from about 30,000 before the nuclear deal was announced, Iranian traders said. Heavy supplies of dollars appeared as speculators anticipated capital flight from Iran would slow with the easing of diplomatic tensions.

At some times on Sunday, nobody in the market was willing to buy dollars, traders said - a dramatic contrast from last year, when the rial lost about a third of its value in a few months.

A firmer outlook for Iran's currency could help to revive its foreign trade in a range of agricultural and consumer goods other than oil, by reducing the foreign exchange risks which have deterred many traders over the past two years.

Also, foreign and Iranian businessmen may become more willing to do deals - even under the existing sanctions framework - if they feel that political trends have shifted in their favour, and that they will not face even harsher sanctions or enforcement from Western governments in the future.

"Up to now, the trend has been towards more restrictions on trade," said Hossein Asrar Haghighi, a founder of the Iranian Business Council in Dubai, which is a major conduit for Iran's trade with the rest of the world.

"What we can say now is that the restrictions are not going to increase still more. And if people do not expect them to increase, they will gradually look at ways to develop business under the current situation."

Dubai's non-oil trade with Iran has shrunk by over a third in the past 18 months, totalling $2.9 billion in the first half of 2013, according to Dubai customs data.

Iranian-born economist Mehrdad Emadi, of the Betamatrix consultancy in London, said Western oil firms and other companies had been contacting Iranian officials and businessmen for months to discuss how trade and investment ties might eventually be restored. Such contacts look set to accelerate in the wake of the Geneva deal.

"Companies have to be careful how they deal with Iran, because they need to maintain an operational relationship with their governments at home. Now they will feel more free to act."

POLICY

The Geneva deal may not launch any extended period of appreciation for Iran's rial, since government officials have indicated excessive currency strength could hurt exports and complicate state finances. Aflani predicted authorities would intervene in the market if needed to prevent the rate from moving too far from 29,500.

But by restraining import costs, a firmer long-term outlook for the currency would help the government deal with one of its biggest economic and political headaches, an inflation rate running at about 40 percent.

And even a modest improvement in economic conditions due to the Geneva deal could give President Hassan Rouhani and his new central bank governor, Valiollah Seif, enough political capital to press ahead with difficult reforms of the economy.

The government of Rouhani's predecessor, President Mahmoud Ahmadinejad, was widely criticised in parliament and the private sector for erratic economic management. Ahmadinejad's critics blamed high inflation partly on wasteful state spending and a failure by the central bank, under political pressure from the government, to keep money supply growth under control.

After taking office in August this year, Rouhani promised to improve economic management and appointed Seif, who said the central bank would be given more independence to focus on controlling inflation and the money supply.

Officials have said in recent weeks that reforms may include tighter monetary policy and cuts in cash subsidies given to rich families - politically sensitive steps that would be easier if Rouhani could point to economic gains during his tenure.

"Because of the entrenched interests, reforming and rationalising economic policy will be very hard," Emadi said. "It could take five years."