  The aim of this paper is to construct families of Calabi--Yau 3-folds without
boundary points with maximal unipotent monodromy and to describe the variation
of their Hodge structures. In particular five families are constructed. In all
these cases the variation of the Hodge structures of the Calabi--Yau 3-folds is
basically the variation of the Hodge structures of a family of curves. This
allows us to write explicitly the Picard--Fuchs equation for the 1-dimensional
families. These Calabi--Yau 3-folds are desingularizations of quotients of the
product of a (fixed) elliptic curve and a K3 surface admitting an automorphisms
of order 4 (with some particular properties). We show that these K3 surfaces
admit an isotrivial elliptic fibration.
