* Asian stock markets : https://tmsnrt.rs/2zpUAr4

* Asia markets swing higher, Nikkei at 3-mth peak

* China surveys show growth at home, subdued exports

* S&P 500 futures bounce, though riots add to economic woe

* Busy week sees ECB meet, U.S. payrolls report

By Wayne Cole

SYDNEY, June 1 (Reuters) - Asian shares pushed to three-month highs on Monday as progress on opening up economies helped offset jitters over riots in U.S. cities and unease over Washington's power struggle with Beijing.

There was also relief that while President Donald Trump began the process of ending special U.S. treatment for Hong Kong to punish China, he left their trade deal intact.

"With specific and verifiable measures against China appearing to be weak, markets may draw hollow consolation that the U.S. is treading carefully," said analysts at Mizuho in a note.

After a cautious start Asian markets were led higher by China on signs parts of the domestic economy were picking up. Hong Kong managed to rally 3.6%, while Chinese blue chips put on 2.4%.

An official business survey from China showed its factory activity grew at a slower pace in May but momentum in the services and construction sectors quickened.

A private survey showed a return to growth in May, though exports remained depressed.

That helped lift MSCI's broadest index of Asia-Pacific shares outside Japan 2.1% to its highest since early March. Japan's Nikkei added 0.7% to also reach a three-month peak.

E-Mini futures for the S&P 500 recovered to be flat, having been down 1% in early trade. EUROSTOXX 50 futures firmed 1.4% and FTSE futures 1.1%.

The resilience was notable given major U.S. cities were cleaning up streets strewn with broken glass and burned out cars as curfews failed to stop confrontations between activists and law enforcement.

The turmoil was a fresh setback for the economy which was only just emerging from a downturn akin to the Great Depression. Following poor data on spending and trade out on Friday, the Atlanta Federal Reserve estimated economic output could drop a staggering 51% annualised in the second quarter.

The May jobs report due out on Friday is forecast to show the unemployment rate surged to 19.8%, smashing April’s record 14.7%. Payrolls are expected to drop by 7.4 million, on top of the 20.5 million jobs lost the previous month.

YEARS, NOT MONTHS

"Current unemployment numbers go far beyond what has been experienced in any post-war recession," wrote Barclays economist Christian Keller in a note.

"To the extent that some sectors may never return to pre-pandemic business-as-usual, labour faces a substantial challenge to reallocate workers," he added. "Such a process could be a matter of years rather than months or quarters and in the meantime it would weigh on consumer demand."