I'm reading about the h-cobordism theorem in boundary dimension 4. Most of the steps are the same as in the classical statement, but finding whitney disks to homotope the 2- and 3-handles into geometric cancelling position proves to be rather difficult.
Assume wo only have a 2- and 3- handle left, in algebraic cancelling position. Also assume that we only have 3 intersection points, so we only need to perform one whitney move. To even get an immersed whitney disk, one needs the following Lemma:
Assume that $P,Q \subset M$ are two embedded surfaces in a 4-dimensional manifold $M$, such that $\pi_1(M) = 0$. Assume we have immersed spheres $P^{\perp},Q^{\perp}$, geometrically dual to $P,Q$ (i.e. $P^{\perp} \pitchfork P = \{ point \}$, $P^{\perp} \pitchfork Q = \emptyset$, $Q^{\perp} \pitchfork Q = \{ point \}$, $Q^{\perp} \pitchfork P = \emptyset$). Then $P\cup Q$ is $\pi_1$-negligible, i.e. $\pi_1(M \setminus (P \cup Q )) = 0$.
Somehow this statement should be "elementary" to prove, because every reference I find just states and uses this fact (and in one it is stated as an "introductory problem"). But I don't even know where to start. Is there a book/article that proves this fact or can someone give me a hint/sketch on where to start?