Colliding bits of material produce light. Even colliding hydrogen clouds produce detectable signatures. If, for the sake of argument, two big bangs occurred and we could see where they met, there would be a large visible region in the universe putting out some sort of photons. (Not necessarily visible ones.)

More subtle things would be visible too, like, yes, interacting gravity fields, but it wouldn't take such clever analysis; the impact points would literally light up in the sky.