Complete axiomatization of relation algebras without ${}^-$ and $\top$
The equational theory of the signature $S=\{\vee,\wedge,.,\epsilon,^\smile\}$ is decidable. See this paper by Andréka and Bredikhin.
The idea is to associate to every term $t$ over $S$ a graph $G_t$. Then Andréka and Bredikhin show that two terms $t$ and $u$ are equivalent iff there is a graph homomorphism from $G_t$ to $G_u$ and a graph homomorphism from $G_u$ to $G_t$. Testing graph homomorphism between finite graphs is decidable, hence the equational theory is also decidable.
The equational theory of $S$ is not finitely axiomatizable, due to the paper of Andréka and Mikulas you have cited. However, contrarily to what is claimed in this paper, the restrictions of the signature to, say, $\{., \cap, \epsilon\}$ is not finitely axiomatizable, as shown in this paper.