  In this article we introduce a family of transverse invariants arising from
the deformations of Khovanov homology. This family includes the invariants
introduced by Plamenevskaya and by Lipshitz, Ng, and Sarkar. Then, we
investigate the invariants arising from Bar-Natan's deformation. These
invariants, called $\beta$-invariants, are essentially equivalent to Lipshitz,
Ng, and Sarkar's invariants $\psi^\pm$. From the $\beta$-invariants we extract
two non-negative integers which are transverse invariants (the $c$-invariants).
Finally, we give several conditions which imply the non-effectiveness of the
$c$-invariants, and use them to prove several vanishing criteria for the
Plamenevskaya invariant $[\psi]$, and the non-effectiveness of the vanishing of
$[\psi]$, for all prime knots with less than 12 crossings.

Geometric Topology