  We discuss analytical properties of partial waves derived from projection of
a 4-legged amplitude with crossed-channel exchanges in the kinematic region of
the direct channel that corresponds to the XYZ peaks in charmonium and
bottomonium. We show that in general partial waves can develop anomalous branch
points in the vicinity of the direct channel physical region. In a specific
case, when these branch points lie on the opposite side of the unitary cut they
pinch the integration contour in a dispersion relation and if the pinch happens
close to threshold, the normal threshold cusp is enhanced. We show that this
effect only occurs if masses of resonances in the crossed channel are in a
specific, narrow range. We estimate the size of threshold enhancements
originating from these anomalous singularities in reactions where the Zc(3900)
and the Zb(10610) peaks have been observed.
