  Any knot in $S^3$ may be reduced to a slice knot by crossing changes. Indeed,
this slice knot can be taken to be the unknot. In this paper we study the
question of when the same holds for knots in homology spheres. We show that a
knot in a homology sphere is nullhomotopic in a smooth homology ball if and
only if that knot is smoothly concordant to a knot which is homotopic to a
smoothly slice knot. As a consequence, we prove that the equivalence relation
on knots in homology spheres given by cobounding immersed annuli in a homology
cobordism is generated by concordance in homology cobordisms together with
homotopy in a homology sphere.
