In this work we study hypergroupoids whose β-relation is transitive, by using the fundamental relations β, β*, δ and δ*. We take several examples, finding the necessary and sufficient conditions such that a quasi-hypergroup has β*=β=δ=δ* (i.e. it is of kind T_1). We shall find that c-completable quasi-hypergroups with identity are of kind T_1 and this gives that every H_v-group with identity is of kind T_1.