  We show, using Wise's equitable sets criterion, that every tubular free by
cyclic group acts freely on a CAT(0) cube complex. We also show that these
groups have a finite index subgroup satisfying the strongest Tits alternative,
which means that every subgroup either surjects a non abelian free group or is
torsion free abelian. In particular the Gersten group is the first known group
virtually having this property but which is not virtually special nor virtually
residually free.
