  We discuss the ribbon-move for 2-knots, which is a local move. Let $K$ and
$K'$ be 2-knots. Then we have: Suppose that $K$ and $K'$ are ribbon-move
equivalent.
  (1) Let ${\mathrm {Tor}} H_1(\widetilde X_K; {\Z})$ (resp. ${\mathrm {Tor}}
H_1(\widetilde X_{K'}; {\Z})$) be the $\Z$-torsion submodule of the Alexander
module $H_1(\widetilde X_K; {\Z})$ (resp. $H_1(\widetilde X_{K'}; {\Z})$). Then
${\mathrm {Tor}} H_1(\widetilde X_K; {\Z})$ is isomorphic to ${\mathrm {Tor}}
H_1(\widetilde X_{K'}; {\Z})$ not only as $\Z$-modules but also as
${\Z}[t,t^{-1}]$-modules.
  (2) The Farber-Levine pairing for $K$ is equivalent to that for $K'$.
  (3) The set of the values of the $\Q/\Z$-valued $\tilde\eta$ invariants for
$K$ is equivalent to that for $K'$.
