  We construct infinite families of topologically isotopic but smoothly
distinct knotted spheres in many simply connected 4-manifolds that become
smoothly isotopic after stabilizing by connected summing with $S^2 \times S^2$,
and as a consequence, analogous families of diffeomorphisms and metrics of
positive scalar curvature for such 4-manifolds. We also construct families of
smoothly distinct links, all of whose corresponding proper sublinks are
smoothly isotopic, that become smoothly isotopic after stabilizing.
