  In 1986, Matveev defined the notion of Borromean surgery for closed oriented
3-manifolds and showed that the equivalence relation generated by this move is
characterized by the pair (first betti number, linking form up to isomorphism).
  We explain how this extends for 3-manifolds with spin structure if we replace
the linking form by the quadratic form defined by the spin structure. We then
show that the equivalence relation among closed spin 3-manifolds generated by
spin Borromean surgeries is characterized by the triple (first betti number,
linking form up to isomorphism, Rochlin invariant modulo 8).
