My furnace and water heater vent pipes connect together and were rusty,...

...so I am replacing them with new? I took the old ones down and made pattern pieces from the old pieces onto the new. Now I have all the pieces, but of course the fit it tricky and so every time I try to put a long piece up, it wants to come loose in places and fall down (and dent a little). Is there a trick to this? I am afraid to fasten them together with screws ahead of time until I know that it is going to fit there. Now there are two holding feet on top of the water heater that have come apart (rusty?) with me fiddling with the pipe that attaches to it. Any ideas? I am tired of wrestling with these pipes.
Every time I try to link one more pipe up, it seems like two pipes fall down. This is frustrating since I thought I was close to done.
Plus my fingers are getting all cut up from the metal where I cut it with tin snips...