I'm starting a study about theory of transformation groups and equivariant cohomology, in what I read several times that Cech cohomology is the most compatible with this theory, but until now I haven't found an explanation for that. I suspect that it has to do with finitistic spaces (or perhaps vice versa), but I am not certain. Can someone explain to me the real reason for that, please?

I'm starting a study about theory of transformation groups and equivariant cohomology, in what I read several times that Čech cohomology is the most compatible with this theory, but until now I haven't found an explanation for that. I suspect that it has to do with finitistic spaces (or perhaps vice versa), but I am not certain. Can someone explain to me the real reason for that, please?