Cohomological n-equivalence of differential graded algebras

For $ngeq 0$, we study a formalism for approximating rational homotopy types of differential graded algebras with cohomological $n$-equivalences, algebra morphisms inducing isomorphisms on cohomology through degree $n$ and a monomorphism in degree $n+1$. We show that localizing with respect to cohomological $n$-equivalences has many fundamental properties in common with localizing with respect to quasi-isomorphisms. Moreover, we show that cohomological $n$-equivalences ``detect' Massey products in degree $n+1$.