  We construct infinitely many smooth oriented 4-manifolds containing pairs of
homotopic, smoothly embedded 2-spheres that are not topologically isotopic, but
that are equivalent by an ambient diffeomorphism inducing the identity on
homology. These examples show that Gabai's recent "Generalized" 4D Lightbulb
Theorem does not generalize to arbitrary 4-manifolds. In contrast, we also show
that there are smoothly embedded 2-spheres that are both equivalent and
topologically isotopic, but not smoothly isotopic.
