I'm not the biggest expert in this stuff, but mostly I hear about picking up leaves and disposing of them off site--it can overwinter in the leaves if you don't (though this probably won't have much effect, sice the disease can also overwinter on twigs, bark etc., and can blow in from other trees). Usually the trees won't die from anthrac unless they are already in bad shape from other factors. Tattar ("Diseases of Shade Trees") recommends spraying bad cases or aesthetically desirable cases with fungicide at or before bud break, then every two weeks until mid-June and additionally after any prolonged wet weather. So you gotta know which trees need it and sell the spraying when there are no symptoms. Good luck.
Keith