  We study the shadowing effect in highly asymmetric diffractive interactions
of left-handed and right-handed W-bosons with atomic nuclei. The target nucleus
is found to be quite transparent for the charmed-strange Fock component of the
light-cone W^+ in the helicity state \lambda=+1 and rather opaque for the c\bar
s dipole with \lambda=-1. The shadowing correction to the structure function
\Delta xF_3 = xF_3^{\nu N}-xF_3^{\bar\nu N} extracted from \nu Fe and \bar\nu
Fe data is shown to make up about 20% in the kinematical range of CCFR/NuTeV.
