By Harriet McLeod

NORTH CHARLESTON, South Carolina, March 31 (Reuters) - A machinists union campaign to organize Boeing Co's South Carolina operations began in earnest on Tuesday, as the company turned over a list of about 3,000 employees eligible for an April 22 organizing vote.

Both sides are stepping up efforts to win support using social and traditional media, and one-on-one campaigning in the strongly anti-union state. Boeing is fighting the International Association of Machinists and Aerospace Workers' (IAM) effort to win a landmark victory by representing workers who build the company's 787 airliner.

The union will use the eligibility list to visit homes and "do as much face to face as possible" to discuss the benefits of organization, said Frank Larkin an IAM spokesman.

Boeing aired two new radio ads this week emphasizing the dangers of strikes and the loss of wages that result.

"Do workers really benefit from strikes?" one of the ads asks. "On all of the strike days, workers didn't receive regular wages, unemployment or healthcare and retirement benefits."

The one-minute spots do not mention that workers typically receive support from a union strike fund.

The IAM is running a campaign out of a rented office on a commercial strip in North Charleston about three miles from the Boeing plant.

The union opened the office a year ago to educate Boeing workers about collective bargaining in a state where only about 4 percent of workers are represented by a union.

Union representatives work phones and hand out black IAM T-shirts and literature. State union leaders, politicians and ministers have signed their support and two plant production workers appear in a pro-union video.

The IAM's campaign focuses on wages, hours, working conditions and dignity on the job, lead organizer Mike Evans said.

They fear raising safety issues, Evans said. "The message is get it done or there's the door."

Boeing recently began scheduling staggered weekend work and Evans said workers told him they have been receiving small bonuses, ranging from a $25 to $500 Wal-Mart gift card.

"We've said for the past five years that we don't believe a union is in the best interests of our teammates, our business, our community nor our state," Boeing spokeswoman Candy Eslinger said in a statement.

The IAM pulled 129,000 workers out on strike in the last decade and would make "over $1 million a year" from South Carolina employees, company websites show.

Under state laws, workers do not have to join a union, if one is formed, and do not have to pay dues, Gordon Lafer, professor of political science at the University of Oregon, said.