Metalbestos pipe identification

What is the best way to ID what kind of metal chimney I have? I am told by the person that installed it 20 or so years ago that it is metalbestos however I tried to connect newer used metalbestos pipe to it and it is about a 1/8" to small to fit on what I currently have. The pipe has a 1-1/4" locking band the newer pipe has a very narrow locking band. The reason I need more pipe is the top section of pipe is pin holed on the outside only the inside is sound and not pitted and I think my chimney needs more hight. Id rather not replace the whole chimney cause the roof is 2 years old.