I strongly urge you not to disturb any asbestos-cement roof that is still in good condition. These are fine roofs that are capable of lasting as long or longer than the brick on the house. Asbestos is a material that is dangerous only when made "friable"--shredded or powdered to make it airborne, allowing you to inhale it. When on your roof, it is locked into a cement shingle, using a cement that is akin to the cement in the sidewalk.
There are probably millions of roofs worldwide that use asbestos shingles, panels, tiles or slates. Their lifespan rivals that of natural slate or clay tile. They are fireproof, rotproof, lighter than slate or tile, and resistant to wind damage, cracking and hail damage.
I installed an asbestos cement roof on my house in 1986 well after the health flap came up about asbestos. Two members of my wife's family died of asbestos-related diseases, one from mesothelioma, the other complications of asbestosis, so I don't underestimate the dangers of the substance. However, there are many other dangerous substances out there will kill you if handled carelessly. Gasoline is a good example--extremely flamable, virtually explosive, poisonous, highly volatile. Yet we all use it in our cars. Asbestos is no different. Leave it on the roof and you'll have no problem.
By the way, you might discover if you check that some of the water pipes in your city are made of asbestos cement pipe--the same substance used for roofing. Here in Houston we have many miles of this kind of pipe in service, with no complaints.
By the way, I am not in the construction business, don't own any asbestos mines, etc. I just think asbestos roofing has been unfairly run out of the market. I've been trying in vain to find more matching asbestos-cement slates to use on an addition I'm planning for my house. My original supplier, Supradur, went bankrupt.