When two black holes collide, they coalesce to form a larger black hole. The event will produce gravitational waves that will have a particular signature that depends on the details of the collision. Black hole merger events are one of the main gravitational wave signals that are being sought at LIGO.
There are a few misconceptions in your question:
1) black holes do not have infinite mass. They in fact have a finite mass. The orbit of the Earth around a black hole with the same mass as the sun's would in fact be identical to the Earth's current orbit. So, the idea of black holes sucking up the space around them is inaccurate.
2) The gravity at the event horizon of a black hole is finite and (generally) inversely proprortional to the mass of the black hole--a sufficiently large black hole would not exert any detectable local strains on objects at all!
3) The geometry of spacetime will be well-defined everywhere except at the central singularity of the black hole. Every observer will report only one direction of time. This direction, in an absolute sense, will be observer dependent, just as it is in special relativity (the rate of aging will depend on speed and position, but will always be well-defined and knowable).