Cement asbestos pipe. Actually once recognized as B-vent for Cat. I gas. Should be removed and replaced with properly sized listed B-vent. Note that when that one screw rots out, the connector can dislodge and vent into the home. Need a venting pro in there. All new vent connector or just run B-vent the entire run, depending upon a lot of factors.

Note, there are the beginings of markings at the bell of the bell and spigot on the transite.
HTH,
Bob

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Keep the fire in the fireplace.