Completeness of the space of topological Anosov flows

Let $M$ be the underlying manifold and let $\mathcal{TA}\mathcal{F}(M)$ denote the space of topological Anosov flows. Equip it with a suitable topology that reflects both uniform convergence of flows and the $d_{\mathrm{An}}$-Cauchy condition on generators.

Completeness. With such a topology, $\mathcal{TA}\mathcal{F}(M)$ forms a complete metric space, or is complete in a relevant sense.

Completeness would provide a useful geometric framework for taking limits of topological Anosov flows. The conjecture remains conditional on choosing a suitable topology, which the source does not specify.