I installed an inside chimney in our first home in the '70s. At the time "triple wall" meant an air thermo siphoning system. Flowing air was used to keep the pipe cool for clearance purposes. I hope that same system is not in use today. IMHO that would be a disaster. A chimney has to be hot to draw and keep the liner relatively clean. Those triple wall units would condense creosote very quickly. I opted for a double wall insulated stainless. And make sure the inner diameter is sufficiently large to draw well when the stove door is open for loading.
Bob