Elliptic and K3 fibrations on double octic Calabi–Yau threefolds

We study fibrations by elliptic curves and K3 surfaces of double octic Calabi–Yau threefolds determined by singular lines and points of multiplicity at least 4 of the defining octic arrangement. As a consequence we conclude that every double octic admits many elliptic and K3 fibrations. We apply descriptions of some K3 fibrations to construct a birational map between elements of two families of double octics.