  We investigate in this work families $(u_\epsilon)_{\epsilon >0}$ of
sign-changing blowing-up solutions of asymptotically critical stationary
nonlinear Schr\"odinger equations of the following type: $$\Delta_g u_\epsilon
+ h_\epsilon u_\epsilon = |u_{\epsilon}|^{p_\epsilon-2} u_\epsilon $$ in a
closed manifold $(M,g)$, where $h_\epsilon$ converges to $h$ in $C^1(M)$.
Assuming that $(u_\epsilon)_{\epsilon >0}$ blows-up as \emph{a single
sign-changing bubble}, we obtain necessary conditions for blow-up that
constrain the localisation of blow-up points and exhibit a strong interaction
between $h$, the geometry of $(M,g)$ and the bubble itself. These conditions
are new and are a consequence of the sign-changing nature of $u_\epsilon$.
