Hi,
That circuit, if it was working with the right values chosen, works like this...
The functions of the three transistors from left to right are:
1. sense/input buffer
2. two phase generator
3. output buffer
It is kinda complicated and that might be because they are trying to use only
transistors rather than ic chips to generate a two phase zero cross signal.
Many zero cross applications can use a single phase zero cross detector
so you should probably consider that first. The deciding factor is just
what kind of circuit you intend to use your zero cross detector with.
For example, you might be able to get away with two diodes and one
resistor (a total of three parts) or two diodes, two resistors, and one
transistor. It all depends on your application circuit so perhaps you should
let us know what you are going to use this for.