Transverse link invariants from the deformations of Khovanov sl3-homology

In this paper we will make use of the Mackaay-Vaz approach to the universal sl(3)-homology to define a family of cycles (called $\beta_3$-invariants) which are transverse braid invariants. This family includes Wu's $\psi_3$-invariant. Furthermore, we analyse the vanishing of the homology classes of the $\beta_3$-invariants and relate it to the vanishing of Plamenevskaya's $\psi$ and Wu's $\psi_3$invariants. Finally, we use the $\beta_3$-invariants to produce some Bennequin-type inequalities.