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A method to simplify 3-bridge projections of links and knots, called a wate move, is discussed in general situation and it is shown what kind of properties of 3-bridge links and knots can be recognized from their projections by wave moves. In particular, it will be proved that every 3-bridge projection of a splittable link or a trivial knot can be transformed into a disconnected one or a hexagon, respectively, by a finite sequence of wave moves. As its translation via the concept of 2-fold branched coverings of S3, it follows that every genus 2 Heegaard diagram of S2 X S2 # L(p, q) or S3 can be transformed into one of specific standard forms by a finite sequence of operations also called wave moves.

The splittability and triviality of 3-bridge links