  We study the effect of mutation on link concordance and 3-manifolds. We show
that the set of links concordant to sublinks of homology boundary links is not
closed under positive mutation. We show that mutation does not preserve
homology cobordism classes of 3-manifolds. A significant consequence is that
there exist 3-manifolds which have the same quantum SU(2)-invariants but are
not homology cobordant. These results are obtained by investigating the effect
of mutation on the Milnor invariants, or equivalently the Massey products.
