  The equitable presentation of the quantum superalgebra
$\mathfrak{osp}_q(1|2)$, in which all generators appear on an equal footing, is
exhibited. It is observed that in their equitable presentations, the quantum
algebras $\mathfrak{osp}_q(1|2)$ and $\mathfrak{sl}_q(2)$ are related to one
another by the formal transformation $q\rightarrow -q$. A $q$-analog of the
Bannai-Ito algebra is shown to arise as the covariance algebra of
$\mathfrak{osp}_q(1|2)$.
