  The goal of the present paper is to find higher genus surgery formulae for
the set of finite-type invariants of homology spheres, and to develop a
companion theory of finite-type invariants to be applied, in a subsequent
publication, to the study of subgroups of the mapping class group. The main
result is to show that six filtrations on the vector space generated by
oriented homology spheres (three coming from surgery on special classes of
links and three coming from subgroups of the mapping class group) are equal. En
route we introduce the notion of blink (a special case of a link) and of a new
subgroup of the mapping class group.
