will show below that for these models also, isotropy is not possible when $\Omega$ tends toward a constant. If now we assume that $\Omega$ diverges, nothing at this stage prevents the asymptotical vanishing of $p_\pm e^{3\Omega}$. Moreover, since $\beta_\pm$ tend toward some constants for a diverging value of $\Omega$, we deduce that $d\beta_\pm/d\Omega\rightarrow 0$ otherwise $\beta_\pm$ would diverge with $\Omega$. Consequently, isotropisation should arise when $\Omega\rightarrow \pm\infty$, $d\beta_\pm/d\Omega$ and $pe^{3\Omega}\rightarrow 0$. These conditions are independent each other and of the considered Bianchi class $A$ models. We will have to check if each of them is respected for each presumed isotropic equilibrium state.\
Let us compare them with isotropisation conditions defined by Collins and Hawking [@ColHaw73]. First, as in this last paper, we have assumed that isotropisation arises when $t\rightarrow \infty$. Second, in the next sections, for each Bianchi models, we will show that isotropisation needs $\Omega\rightarrow -\infty$. This is the first condition that defines isotropisation in Collins and Hawking’s paper and which implies that Universe expands indefinitely. Third, the fact that $d\beta_\pm/dt$ and $d\beta_\pm/d\Omega$ tend toward zero satisfies their third condition meaning that “the anisotropy in the locally measured Hubble constant tends to zero”. Thus from the necessary but not 