We don't know and you can make up the effect you want. The answer given above correctly sums up our current understanding of black holes and gravity. However, currently we can't reconcile our understanding of gravity (which explains black holes) with our understanding of quantum mechanics (which explains mater/antimatter interaction). In other words, "nothing will happen" ist not something we know but something we'd need to test in an experiment.
If you want a spectacular effect, you can make one up: During matter/antimatter annihilation, the mass/energy stops to have gravity for short moments (due to quatnum gravity effects we have not been able to observe yet, because they are to weak when we do these experiments with single atoms in a collider). This allows some mass and or radiation to escape (either in direction with the spin of the BH, or as a jet along the axis of rotation). Also the on/off sends strong gravitational waves. 343
Some of the emitted matter/energy lumps may be dense enough to form black holes themselves, they may loose momentum when interacting with the accretion disks and fall back into the large BH ...
The shape will be weird - wikipedia has this to say about a black hole merger: "As two black holes approach each other, a ‘duckbill’ shape protrudes from each of the two event horizons towards the other one. This protrusion extends longer and narrower until it meets the protrusion from the other black hole. At this point in time the event horizon has a very narrow X-shape at the meeting point. The protrusions are drawn out into a thin thread. The meeting point expands to a roughly cylindrical connection called a bridge."
One question that a reader with a good grasp of physiscs will have is when this cataclysm will happen - I think our best guess according to current physics is that time will stop inside the event horizon due to gravitationl time dilation. Short 'hiccups' in gravity will also stop this dilation.
For story purposes it would be a bad idea if the affair becomes a completly naked singularity (20 SM matter annihiliation?), however I think you can make up a mechanism with that only partially ot for short moments 'opens' the event horizon.
For scientists this will be very exciting because it is the first chance to look at a naked singularity. Problem is: Noone can quite predict what will happen, so noone knows the safe distance to observe the event! 43