  The flat plumbing basket presentation of a link is introduced by Furihata,
Hirasawa and Kobayashi. In this paper, we show that the pass-equivalence and an
equivalence introduced by using the flat plumbing basket presentation are the
same relation. Furthermore, we obtain an evaluation of the minimal number of
bands used for the flat pluming basket presentation for a knot coming from the
degree of the Alexander polynomial and the three genus of the knot.
