Weak generalized Property R conjecture for 4-dimensional 2-handlebodies

Let $n$ be a nonnegative integer. Suppose that attaching $n$ $2$-handles to $B^4$ gives a $4$-manifold $W$ whose boundary is

$$\partial W\cong \#_{n}(S^{1}\times S^{2}).$$

Weak generalized Property R conjecture. Then

$$W\cong \natural_{n}(S^{2}\times D^{2}).$$

This is presented as a possibly weaker form of the generalized Property R conjecture. The proposition preceding it shows that the generalized conjecture would imply the standard $S^4$ conclusion for homology $4$-spheres with handle structures containing no $3$-handles; the paper later states that this weak conjecture is equivalent to that homology-$4$-sphere conjecture.