the initial singularity, the Bianchi I solution in vacuum is Kasner-like and the presence of a perfect fluid is negligible. In [@BK_Bianchi], it has been shown instead that in the presence of a shear viscous contribution the situation significantly changes but a Kasner-like solution still exists and it is characterized by a vanishing behavior of the energy density. Here, we want to verify if such a peculiarity survives when the Eckart representation of the viscous fluid is upgraded in terms of the Lichnerowicz causal reformulation. It is rather easy to realize via a simple asymptotic analysis, that the ansatz in [@Disc1] fails in the region of small value of $\rho$. In fact, the latter predicts $F\sim\rho R^3$ and clearly vanishes near the singularity if $\rho\sim0$ (as $R^3$ is going naturally to zero toward the singularity). In investigating the solutions in this region we need therefore to search for a different representation of $F$. A possibility is to infer its form by picking the case of an incompressible fluid. From equation (\[incomp\]) and by using the line-element (\[metricaBI\]), one immediately gets the following expression for $F$ $$F=\frac{F_{0}}{R^{3}},$$ where we used the convention for which the subscript number denotes an integration constant. 