In Smale's On the structure of manifolds paper there is his relative version of the h-cobordism theorem, specifically Theorem 3.1 (and 1.4). Roughly speaking this concerns the situation where one has an h-cobordism of pairs, and you want some compatibility between the ambient product structure and the submanifold product structure.

I find I don't think about this theorem often, but every once and a while I do need to use it. Each time I return to it, I take considerable time to process how it can be used -- somehow it is not worded in a way that plays well with my way of thinking about things.

I imagine I am not the only person with this problem.

Are there other expositions of the relative h-cobordism theorem in the literature?