  We investigate the blow-up behavior of sequences of sign-changing solutions
for the Yamabe equation on a Riemannian manifold $(M,g)$ of positive Yamabe
type. For each dimension $n\ge11$, we describe the value of the minimal energy
threshold at which blow-up occurs. In dimensions $11 \le n \le 24$, where the
set of positive solutions is known to be compact, we show that the set of
sign-changing solutions is not compact and that blow-up already occurs at the
lowest possible energy level. We prove this result by constructing a smooth,
non-locally conformally flat metric on space forms $\mathbb{S}^n/\Gamma$,
$\Gamma \neq \{1\}$, whose Yamabe equation admits a family of sign-changing
blowing-up solutions. As a counterpart of this result, we also prove a sharp
compactness result for sign-changing solutions at the lowest energy level, in
small dimensions or under strong geometric assumptions.
