For many years, Downtowners have waited for the long ago-promised connection between the Hudson and East River bike paths. The long dormant project has recently moved back to the front burner. The Battery Park Bike Path, marked, above, will give bikers a clear route through Battery Park from the Hudson River to East River waterfronts. “The bikeway is a top priority,” said Warrie Price, president of the Battery Conservancy. “It will unify the entire Battery.” The design-development phase of the project is complete, but it was on hold while the Metropolitan Transportation Authority tore up Battery Park to expand the South Ferry subway station. The M.T.A. also agreed to pay the city Parks Dept. for park improvements. Construction on the bike path is expected to start in 2009 and the path will open in 2010.