Is there a simple construction of a Sullivan minimal model $\Lambda U \rightarrow V$ in the case that $H^1(V)\neq 0$? Do you have a reference? I envisage a degree-wise construction as in the case of $H^1(V)=0$ explaining how to deal with the new phenomenon. The existence is proven very generally in *Felix, Halperin, Thomas, Rational Homotopy Theory* but I find the proof very complicated and not transparent enough in this simple case (they prove that relative Sullivan models exist and that any relative Sullivan algebra is isomorphic to a product of a minimal relative Sullivan algebra and an acyclic algebra)



Sullivan minimal model in the case of $H^1(V)\neq 0$
Gelfand and Manin explain it very nicely in their book "Methods of Homological Algebra", last chapter.


