When I see an animation of two colliding black holes anywhere, it looks like two merging beads of water. But why would the event horizon form a bridge during collision? There is no material flowing in-between. Wouldn't the event horizons "push" each-other away as they merge?(the effect not the black hole itself) For what I understand the gravity would poorly, but surely, be canceled out. Wouldn't this "push" only disappear from view as they got significantly closer, where it still exists but is trapped in a much larger one?
Just to make sure, as I see the similar questions: I don't mean what happens as they collide, but rather why isn't this portrayed if it does this effect at all?