  In this paper we classify the elliptic fibrations on K3 surfaces which are
the double cover of a blow up of $\mathbb{P}^2$ branched along rational curves
and we give equations for many of these elliptic fibrations. Thus we obtain a
classification of the van Geemen--Sarti involutions (which are symplectic
involutions induced by a translation by a 2-torsion section on an elliptic
fibration) on such a surface. Each van Geemen--Sarti involution induces a
2-isogeny between two K3 surfaces, which is described in this paper.
