  We study the oriented exchange graph $\textrm{EG}^\circ(\Gamma_{N}\,Q)$ of
reachable hearts in the finite-dimensional derived category
$\mathcal{D}(\Gamma_{N}\,Q)$ of the CY-$N$ Ginzburg algebra $\Gamma_{N}Q$
associated to an acyclic quiver $Q$. We show that any such heart is induced
from some heart in the bounded derived category $\mathcal{D}(Q)$ via some
`Lagrangian immersion'
$\mathcal{L}:\mathcal{D}(Q)\to\mathcal{D}(\Gamma_{N}\,Q)$. We build on this to
show that the quotient of $\textrm{EG}^\circ(\Gamma_{N}\,Q)$ by the
Seidel-Thomas braid group is the exchange graph $\textrm{CEG}_{N-1}(Q)$ of
cluster tilting sets in the (higher) cluster category $\mathcal{C}_{N-1}(Q)$.
As an application, we interpret Buan-Thomas' coloured quiver for a cluster
tilting set in terms of the Ext quiver of any corresponding heart in
$\mathcal{D}(\Gamma_{N}\,Q)$.
