$\mathcal F$-Transitivity of Backward Shifts on Lattice Graphs

We study $\mathcal F$-transitivity of backward shifts on finite- and infinite-width directed lattice graphs. For the unilateral and bilateral finite-width lattices on weighted $\ell^p$- or $c_0$-spaces, we obtain exact weight characterizations of $\mathcal F$- and $\widetilde{\mathcal F}$-transitivi