LCG Moves in Crystallizations

From a point of view of crystallizations as extended Heegaard diagrams, we introduce LCG ( linear cut and glue) moves with which we investigate relations between geometric T-transformations and crystallization moves. As applications of LCG moves, we verify various equivalences of Lins' crystallizations r _i ⁿ by means of LCG moves. In particular, we show that the two inequivalent Heegaard splittings of the Brieskorn homology sphere (2,3,7) are equivalent under single stabilization of each Heegaard splitting by explicitly showing LCG moves associated with the stable equivalence.