  We write down an explicit operator on the chiral de Rham complex of a
Calabi-Yau variety $X$ which intertwines the usual $\mathcal{N}=2$ module
structure with its twist by the spectral flow automorphism of the
$\mathcal{N}=2$, producing the expected \emph{spectral flow equivariance}.
Taking the trace of the operators $L_{0}$ and $J_{0}$ on cohomology, and using
the obvious interaction of spectral flow with characters, we obtain an explicit
categorification of ellipticity of the elliptic genus of $X$, which is well
known by other means.
