Let \(E\) and \(E'\) be equivalence relations on \(X\) and \(X'\), respectively. A function \(U:X'\to X\) is a reduction of \(E'\) to \(E\) if \(x\mathrel{E'}y\leftrightarrow U(x)\mathrel{E}U(y)\) for all \(x,y\in X'\). If \(E\) is the equality relation on \(X\) the reduction \(U\) is called an enumeration. If the reduction \(U\) is one-to-one it is called an embedding. The main result of the paper says that every real-ordinal definable equivalence relation on the set of reals in the Solovay model either has a real-ordinal definable enumeration of equivalence classes by elements of \(2^{<\omega_1}\), or there exists a continuous embedding of Vitali equivalence relation to \(E\). Moreover, if \(E\) is \(\Sigma^1_1\) (resp. \(\Sigma^1_2\)), then the reduction is \(\Delta^1_1\) (resp. \(\Delta^1_2\)). The proof is based on a topology \(\mathcal T\) generated by ordinal definable sets, and either a given equivalence relation is closed in the product topology \({\mathcal T}^2\) or not which leads to the two cases in the theorem.