Comparisons of benchmark equivalence relations

We determine the Borel-reducibility comparison of each pair of $\mathbfΠ^0_3$ benchmark equivalence relations in Gao's monograph. The additional comparisons we prove are $E_\infty\leq_B c_0$, $E_\infty\nleq_B\ell_p$ for $2<p<\infty$, $\ell_p\nleq_B{\equiv_m}$ for $2<p<\infty$, $c_0\nleq_B{\equiv_m}$