  We study the Goussarov-Habiro finite type invariants theory for framed string
links in homology balls.
  Their degree 1 invariants are computed: they are given by Milnor's triple
linking numbers, the mod 2 reduction of the Sato-Levine invariant, Arf and
Rochlin's $\mu$ invariant. These invariants are seen to be naturally related to
invariants of homology cylinders through the so-called Milnor-Johnson
correspondence: in particular, an analogue of the Birman-Craggs homomorphism
for string links is computed.
  The relation with Vassiliev theory is studied.
