  We have recently demonstrated that by expanding in small distance from the
magnetic axis compared to the major radius, stellarator shapes with low
neoclassical transport can be generated efficiently. To extend the utility of
this new design approach, here we evaluate measures of magnetohydrodynamic
interchange stability within the same expansion. In particular, we evaluate
magnetic well, Mercier's criterion, and resistive interchange stability near a
magnetic axis of arbitrary shape. In contrast to previous work on interchange
stability near the magnetic axis, which used an expansion of the flux
coordinates, here we use the inverse expansion in which the flux coordinates
are the independent variables. Reduced expressions are presented for the
magnetic well and stability criterion in the case of quasisymmetry. The
analytic results are shown to agree with calculations from the VMEC equilibrium
code. Finally, we show that near the axis, Glasser, Greene, & Johnson's
stability criterion for resistive modes approximately coincides with Mercier's
ideal condition.
