  The spherically symmetric dust model of Lemaitre-Tolman can describe
wormholes, but the causal communication between the two asymptotic regions
through the neck is even less than in the vacuum
(Schwarzschild-Kruskal-Szekeres) case. We investigate the anisotropic
generalisation of the wormhole topology in the Szekeres model. The function
E(r, p, q) describes the deviation from spherical symmetry if \partial_r E \neq
0, but this requires the mass to be increasing with radius, \partial_r M > 0,
i.e. non-zero density. We investigate the geometrical relations between the
mass dipole and the locii of apparent horizon and of shell-crossings. We
present the various conditions that ensure physically reasonable
quasi-spherical models, including a regular origin, regular maxima and minima
in the spatial sections, and the absence of shell-crossings. We show that
physically reasonable values of \partial_r E \neq 0 cannot compensate for the
effects of \partial_r M > 0 in any direction, so that communication through the
neck is still worse than the vacuum.
  We also show that a handle topology cannot be created by identifying
hypersufaces in the two asymptotic regions on either side of a wormhole, unless
a surface layer is allowed at the junction. This impossibility includes the
Schwarzschild-Kruskal-Szekeres case.
