Our neighbour saw a rat going in one of the pipes sticking out from our roof...Ewwwww.

We checked and there are no holes around the pipe. None of the vents have a cover. I would like to put covers on the vents. I saw some plastic covers, but they can't be used on gas exhaust. One bathroom is beside the furnace/AC/Water Heater location. There are 6 pipes there - I think one each for toilet/2 sinks/bath tub ?? The other 2 might be for the furnace. How do I know which pipes are plumbing vents? Silly question, but I have no idea.

Should I use a plastic cover or just clamp wire mesh over the vents?

Thanks for any help.