If two singularities, one of matter and one of anti-matter, were to merge, the particles and antiparticles would likely annihilate before the collision, ceasing to exist. If they did collide within the event horizon, the resulting energy would also fall into the singularity, leaving no observable effect outside. The discussion highlights that even in a hypothetical scenario, the merger would not yield any special outcomes beyond the typical matter-antimatter annihilation. Additionally, the conversation touches on the principle of mass-energy equivalence, explaining how energy can be converted into mass during particle collisions. Overall, the merging of matter and anti-matter singularities would not produce observable results due to the nature of black holes.