Can we exit the event horizon of merging black holes? I have an intuitive scenario. Consider we have a spaceship just below the event horizon of a BH, which is merging with another black hole.
Finally, the singularities merge and we have a single black hole again.
But, in the transient stage, it is unclear to me if a timelike world-line would exist to leave the system.
I suspect, the metric is probably far too complex for an analytical solution, but in the worst case, it could be maybe solved numerically.
As far I know, black hole merges are examined mainly in an inspiral scenario. I suspect, maybe the escape is possible only if they have a hyperbolic-like orbit (i.e. there is no inspiral, but they simply collide).
Is it possible?
 A: No. When they merge their horizons will change shape, and eventually become the static or stationary shape of a BH horizon. Nothing inside either horizon while this is happening can escape. At all times the timelike curves stay inside, and the deformed horizons are where the lightlike curves end up. In each, and after they merge. 
The area of each horizon right before they merge can not be smaller than before, as area is proportional to entropy which must increase or stay the same. All deformations will increase it (or be the same, but probably increase). At no times can lightlike Curves escape because of some deformation, and much less timelike curves. 
I assume you meant you were right inside before. If you meant right outside anything can happen, now you'd have to take the ergospehereergosphere into account, and if inside it also probably no but I am a not sure. 
There was similar question posted maybe 3 or so months ago, not in my saved list so I can't give you the reference. There were some answers. 
A: Classically speaking, since total BH evaporation takes finite time, yet being at the event horizon stops all time (in your IRF), the black hole will evaporate before you can get to the event horizon.
