  Let $\widetilde{K}$ be a two-periodic braid and let $K$ be its quotient. In
this paper we show there is a spectral sequence from the next-to-top winding
number grading of the sutured annular Khovanov homology of the closure of
$\widetilde{K}$ to the next-to-top winding number grading of the sutured
annular Khovanov homology of the closure of $K$.
