Two spaces $X$ and $Y$ are said to be rationally homotopy equivalent, written $X \sim_{\mathbb{Q}} Y$, if their rationalizations $X_{\mathbb{Q}}$ and $Y_{\mathbb{Q}}$ are homotopy equivalent. Moreover, to a simply connected topological space $X$, one may associate a certain algebraic object called a minimal model, written $\mathcal{M}_X.$ Importantly, $X \sim_{\mathbb{Q}}Y$ if and only if $\mathcal{M}_X \cong \mathcal{M}_Y.$
Known references. Let $X$ be a nilpotent space with minimal model $\mathcal{M}_X = (\Lambda V, d)$. The relationship between the minimal model of $X$ and the Postnikov tower of $X$ is known [Section 2.5.4 of Félix, Oprea, Tanré, Algebraic Models in Geometry, Oxford University Press, 2008].
Question. Consider a fibration $F \longrightarrow E \overset{p}\longrightarrow B$, where $B,E,$ and $F$ are all simply connected. Does anyone know of a reference explaining the relationship between the minimal model of the fibration $p$ and its Moore--Postnikov tower? In particular, what can we understand about the $k$-invariants of the (integral) Moore--Postnikov tower of $p$ from the $k$-invariants of the Moore--Postnikov tower of the rationalization of $p$?
