  We present a detailed study of spectrally flowed four-point functions in the
SL(2,$\mathbb{R}$) WZW model, focusing on their conformal block decomposition.
Dei and Eberhardt conjectured a general formula relating these observables to
their unflowed counterparts. Although the latter are not known in closed form,
their conformal block expansion has been formally established. By combining
this information with the integral transform that encodes the effect of
spectral flow, we show how to describe a considerable number of $s$-channel
exchanges, including cases with both flowed and unflowed intermediate states.
For all such processes, we compute the normalization of the corresponding
conformal blocks in terms of products of the recently derived flowed
three-point functions with arbitrary spectral flow charges. Our results
constitute a highly non-trivial consistency check, thus strongly supporting the
aforementioned conjecture, and establishing its computational power.
