Two-critical-point obstruction to a trivial cobordism ($\mu =\lambda +1,S_U(p)\cdot S_L(q)=\pm 1$)

If a cobordism Morse function on a trivial cobordism has exactly two critical points, its relative Morse chain complex has two generators and must be acyclic. Their indices therefore differ by one. The only differential is multiplication by the signed intersection of the lower point's belt sphere with the higher point's attaching sphere in a common regular level. A two-term complex of copies of $\mathbb{Z}$ is acyclic exactly when that integer is a unit. Algebraic intersection is therefore a necessary condition; it is not by itself a geometric handle-cancellation statement.