  In this paper, we prove the blow-up invariance for Hodge-Witt sheaves with
modulus, which is a generalization of a result of Koizumi for Witt sheaves and
that of Kelly-Miyazaki and Koizumi for Hodge sheaves. As a consequence, we
obtain the representability of Hodge-Witt sheaves with modulus in the category
of motives with modulus under the assumption of resolution of singularities.
