  We refine Matveev's result asserting that any two closed oriented 3-manifolds
can be related by a sequence of borromean surgeries if and only if they have
isomorphic first homology groups and linking pairings. Indeed, a borromean
surgery induces a canonical isomorphism between the first homology groups of
the involved 3-manifolds, which preserves the linking pairing. We prove that
any such isomorphism is induced by a sequence of borromean surgeries. As an
intermediate result, we prove that a given algebraic square finite presentation
of the first homology group of a 3-manifold, which encodes the linking pairing,
can always be obtained from a surgery presentation of the manifold.
