If the coil is located on the back of the zipper instead of the front it is an Invisible Zipper. Metal zippers consist of individual metal teeth. They are typically made from nickel, brass, aluminum and manganese.
Repair costs generally range from about $2000.00 to $4500.00 per flue or more! In a Real Estate transaction, you may have the opportunity to negotiate defects that are disclosed as part of the inspection process.
I had such a repair done to my almost 100 year old chimney for about $300. He tuckpointed and replaced bricks that had fallen off the top course or two. We had the fallen bricks for him to use. I would have done it myself, but I was afraid to climb to the top of our very steep roof.