  We investigate here linear stability in a canonical three-dimensional
boundary layer generated by the superposition of a spanwise pressure gradient
upon an otherwise standard channel flow. As the main result, we introduce a
simple coordinate transformation that enables the complete description of modal
and non-modal stability using previous results on Poiseuille flow. We leverage
this insight to derive closed forms for some relevant stability metrics. In
particular, the critical Reynolds number for exponential-in-time growth is
found to monotonically decrease with the strength of the cross-flow. A suitably
chosen re-scaling, however, shows that the stability characteristics ultimately
approach those of channel flow, despite the presence of a non-zero spanwise
shear. Unstable eigenmodes akin to the Tollmien-Schlichting wave are found to
propagate along the direction of the net flow. From a non-modal perspective,
the maximal transient (algebraic) growth increases quadratically with the
spanwise pressure differential and, similar to two-dimensional flows, is fueled
by the lift-up effect. In this regard, the linear energy budget highlights a
dramatic increase in energy production against the spanwise shear.
