  Within the framework of a generalized collinear factorization for multiple
parton scattering in nuclear medium, twist-4 contributions to DIS off a large
nucleus can be factorized as a convolution of hard parts and two-parton
correlation functions. The hard parts for the quark scattering in the
light-cone gauge correspond to interaction with a transverse (physical) gluon
in the target, while they are given by the second derivative of the cross
section with a longitudinal gluon in the covariant gauge. We provide a general
proof of the equivalence of the hard parts in the light-cone and covariant
gauge. We further demonstrate the equivalence in calculations of twist-4
contributions to semi-inclusive cross section of DIS in both lowest order and
next leading order. Calculations of the nuclear transverse momentum broadening
of the struck quark in the light-cone and covariant gauge are also discussed.
