The Marvel Heroes Secret Wars are usually cited as "Marvel's Crisis on Infinite Earths" despite the fact that that the Marvel series ran from May 1984 to April 1985 and COIE ran from April 1985 to March 1986. I'm not sure why DC is given so much credit when Marvel did theirs a full year earlier.

http://tvtropes.org/pmwiki/pmwiki.php/Main/CrisisCrossover

However, it's true that Marvel and DC sort of fed off of each other's successes. Infinity Gauntlet (Series) might not have been greenlit or pushed as hard without the success of COIE. But COIE might not have blah blah blah without Marvel Heroes Secret Wars.