covering $\{B_i\}$ of $M_*$ by balls so that all their pairwise intersections are also contractible. Let $\Lambda(\mathfrak p_{\Omega_*})$ be the space of periodic curves $\gamma\in\Lambda_{\mathfrak h}(\Sigma)$ with the property that $\mathfrak p_{\Omega_*}(\gamma)$ is contained in some $B_i$ and there is a path $\{\gamma_r^\mathrm{short}\}\in\widetilde\Lambda_{\mathfrak h}(\Sigma)$ entirely contained in $\mathfrak p_{\Omega_*}^{-1}(B_i)$ with $\gamma^\mathrm{short}_1=\gamma$. If $\Omega\in\Xi^2_C(\Sigma)$, we set $$\mathcal A_{\Omega}:\Lambda(\mathfrak p_{\Omega_*})\to{{\mathbb R}},\qquad\mathcal A_\Omega(\gamma):=\widetilde{\mathcal A}_{\Omega}\big([\delta_r\#\gamma^\mathrm{short}_r]\big),\qquad \gamma^\mathrm{short}_1=\gamma.$$ Here, the symbol $\#$ denotes the concatenation of paths, $\{\delta_r\}$ is any path of periodic curves such that $\delta_1=\gamma_0^\mathrm{short}$, and for every $r\in[0,1]$, $\delta_r$ is an oriented $\mathfrak p_r$-fibre, where $\{\mathfrak p_r\}$ is a path of oriented $S^1$-bundles connecting $\mathfrak p_0$ with $\mathfrak p_1=\mathfrak p_{\Omega_*}$. We define $$\mathcal A_{\min}(\Omega):=\inf_{\gamma\in\mathcal X(\Omega)\cap\Lambda(\mathfrak p_{\Omega_*})}\mathcal A_{\Omega}(\gamma),\qquad \mathcal A_{\max}(\Omega):=\sup_{\gamma\in\mathcal X(\Omega)\cap\Lambda(\mathfrak p_{\Omega_*})}\mathcal A_{\Omega}(\gamma).$$ By [@Gin87 Section III] or [@APB14 Section 3.2], if $\Omega\in \mathcal S_C(\Sigma)$ is $C^1$-close to $\Omega_*$, the set $\mathcal X(\Omega)\cap\Lambda(\mathfrak p_{\Omega_*})$ is compact and non-empty. Furthermore, the numbers $\mathcal A_{\min}(\Omega)$ and $\mathcal A_{\max}(\Omega)$ are finite and vary $C^1$-continuously with $\Omega$.

\[con:lsios\] Let $\Omega_*$ be a Zoll odd-symplectic form with cohomology class $C\in H^2_{{\mathrm{dR}}}(\Sigma)$. There is a $C^{k-1}$-neighbourhood $\mathcal U$ of $\Omega_*$ in $\mathcal S_C(\Sigma)$ with $k\geq 2$ such that $$P(\mathcal A_{\min}(\Omega))\leq{{\mathfrak{Vol}}}(\Omega)\leq P(\mathcal A_{\max}(\Omega)),\qquad \forall\,\Omega\in \mathcal U.$$ The equality holds in any 