  We consider a family of smooth perturbations of unipotent flows on compact
quotients of $\text{SL}(3,\mathbb{R})$ which are not time-changes. More
precisely, given a unipotent vector field, we perturb it by adding a
non-constant component in a commuting direction. We prove that, if the
resulting flow preserves a measure equivalent to Haar, then it is parabolic and
mixing. The proof is based on a geometric shearing mechanism together with a
non-homogeneous version of Mautner Phenomenon for homogeneous flows. Moreover,
we characterize smoothly trivial perturbations and we relate the existence of
non-trivial perturbations to the failure of cocycle rigidity of parabolic
actions in $\text{SL}(3,\mathbb{R})$.
