  Using the techniques introduced by Corvaja and Zannier we solve the non-split
case of the geometric Lang-Vojta Conjecture for affine surfaces isomorphic to
the complement of a conic and two lines in the projective plane. In this
situation we deal with sections of an affine threefold fibered over a curve,
whose boundary, in the natural projective completion, is a quartic bundle over
the base whose fibers have three irreducible components. We prove that the
image of each section has bounded degree in terms of the Euler Characteristic
of the base curve.
