One can also wonder what happens when we start from an arbitrary orientable flat $3$–manifold instead of a $3$–torus. There are $6$ of these: in the notation of [41, §3.5] they are $\mathcal{G}_{1}=T^{3}$, $\mathcal{G}_{i}=T^{3}/\mathbb{Z}_{i}$ for $i=2,3,4$, $\mathcal{G}_{5}=T^{3}/\mathbb{Z}_{6}$ and $\mathcal{G}_{6}=T^{3}/(\mathbb{Z}_{2}\times\mathbb{Z}_{2})$. Only $\mathcal{G}_{1}$ has $b_{1}=3$, $b_{1}(\mathcal{G}_{i})=1$ in all other cases except for $\mathcal{G}_{6}$ which has purely torsion first homology [29, Equation (2.5)]. By working on the $3$–torus equivariantly with respect to a finite group action, the Gibbons–Hawking construction then yields (incomplete) Ricci-flat metrics on circle bundles over a punctured flat $3$–manifold $M$ which are hyperkähler only when $M=T^{3}$, Kähler if $M=\mathcal{G}_{i}$ for $i=2,3,4,5$ and have generic holonomy when $M=\mathcal{G}_{6}$. Moreover, Luft–Sjerve [29, Theorem 1.1] have shown that only $\mathcal{G}_{1},\mathcal{G}_{2}$ and $\mathcal{G}_{6}$ admit an involution with finitely many fixed points ($8$, $4$ and $2$ of them, respectively). Hence only in these $3$ cases are we able to construct background Ricci-flat metrics that can be extended to complete metrics by gluing in copies of ALF spaces of cyclic and dihedral type. On the other hand, Hitchin [22, Theorem 1] showed that the only Ricci-flat $4$–manifolds covered by the K3 surface are the Enriques surfaces (quotients of a K3 surface by an involution without fixed points) with their Kähler Ricci-flat metrics and the quotient of an Enriques surface by an anti-holomorphic involution without fixed points. Carrying out our gluing construction equivariantly with respect to a finite group action then allows us to produce collapsing sequences of Ricci-flat metrics on an Enriques surface (the metrics are Kähler in this case) and its quotient by an anti-holomorphic involution: the collapsed limit is $\mathcal{G}_{2}/\mathbb{Z}_{2}$ and $\mathcal{G}_{6}/\mathbb{Z}_{2}$, respectively, and ALF gravitational instantons appear as “bubbles”.