What is "semi-s-cobordism"

In mathematics, a cobordism (W, M, M) of an (n + 1)-dimensionsal manifold (with boundary) W between its boundary components, two n-manifolds M and M, is called a semi-s-cobordism if (and only if) the inclusion $M \hookrightarrow W$ is a simple homotopy equivalence (as in an s-cobordism) but the inclusion $M^- \hookrightarrow W$ is not a homotopy equivalence at all.