The merging process of two amphiphilic cylindrical micelles has been simulated using a coarse grained model in which amphiphiles are represented as chains of one head particle and four tail particles. In our set-up with twisted boundary conditions, a ring-shaped worm is effectively entangled with itself. Upon stretching the box, putting the worms under tension, a fusion into an H-like structure is observed, which eventually transforms into an almost tensionless structure with two freely gliding Y-junctions. The tensions on the worms never reach the point where scission becomes an alternative to fusion. We end with a short discussion of the possible implications of these observations.