How can I best connect this metal gas flue pipe to the old asbestos cement chimney pipe?
What I did.  I purchased a new flexible elbow and borrowed a five blade HVAC crimper from my local Tool Library.

I carefully spray painted the transite asbestos flue pipe, just to make it a bit less powdery if touched. Then crimped the standard 5&quot; pipe down to about 4.5&quot;, and sent it home with improvements to the straps holding the entire pipe up.  I wore a P100 purple mask the entire time.

This should hold things for now.  It's impractical to replace the pipe itself, but one day a heat pump or direct vent gas furnace will come, and this pipe will be obsolete.