A surgery representation of 3-dimensional homology spheres (Q1377220)

The author proves that for any 3-dimensional homology sphere, there exists a sequence of homology spheres \(M_0,M_1,\dots, M_s\), such that \(M_0=M\) and each \(M_i\) is a result of \(\pm 1\) surgery of \(M_{i-1}\) along a knot \(K_{i-1}\subset M_{i-1}\). Moreover, the author proves that the results of surgeries of \(S^3\) along two framed links \(L\) and \(L'\) are the same if and only if \(L\) can be changed to \(L'\) by a sequence the Kirby moves of types I and II.