My understanding is that one thinks to rational homotopy theory for computational advantage. However, thinking about things in terms of localizations still lacks some amount of intuition for me.

In particular, if $f,g$ are continuous functions and $\gamma$ is localization functor by rational homotopy equivalence and $\gamma(f)=\gamma(g)$, is there something I can say analogous to continuously ("rationally"?) transforming $f$ to $g$".

Thanks!