Slice and sort a sequence of surfaces keeping the central part

Hi all, I have this problem:
I would like to slice each brep with the near ones (and only the near ones: such as the first with the second, the second with the first and the third, the third with the second and the fourth  etc.), and I want to achieve the result on the right (if it can help I could have a polilyne parallel to each brep)

Maybe the polilyne is not necessary
All consecutive breps have tangent perimeters like in the example
And the number of breps can change in the input

I don't know if I have been clear enought, it's an hard problem to figure out