new basepoint, for which the following holds: there is an arc $z_{t}$ from $z_{1}$ to $z_{2}$ on the surface $\Sigma $, which is disjoint from all curves $\beta _{i}$ and from all curves $\alpha _{i}$ appart from $\alpha _{j}$. Then for any generator $\mathbf{x}\in {\mathbb {T}}_{\alpha }\cap {\mathbb {T}}_{\beta }$ we have $$\mathfrak{s}_{z_{2}}(\mathbf{x})-\mathfrak{s}_{z_{1}}(\mathbf{x})=\alpha _{j}^{*}\;,$$ where $\alpha _{j}^{*}\in H^{2}(Y;{\mathbb {Z}})$ is the Poincaré dual of the homology class in ${Y_{m,n}}$ induced by the curve $\gamma $ in $\Sigma $, for which $\alpha _{j}\cdot \gamma =1$ and whose intersection number with any other curve $\alpha _{i}$ for $j\neq i$ equals $0$.

**Class $\mathfrak{s}_{0}+\mu _{1}+\mu _{2}$**\
We change the basepoint $z_{1}\in D_{5}$ for a new basepoint $z_{2}\in D_{2}$. By Lemma \[lemaz\] the $\sp $ structure $\mathfrak{s}_{0}+\mu _{1}=\mathfrak{s}_{z_{1}}(\{x_{m-2},b_{1},f_{1}\})$ changes to $\mathfrak{s}_{0}+\mu _{1}+\mu _{2}=\mathfrak{s}_{z_{2}}(\{x_{m-2},b_{1},f_{1}\})$. In the new $\sp $ structure we have the same generators as in the class $\mathfrak{s}_{0}+\mu _{1}$, but with a new relative grading, induced by the basepoint $z_{2}$: $$\xymatrix{\quad & \{x_{m-2},b_{1},f_{2}\}\ar@{.>}[d]\\
\{x_{m},c_{1},e_{1}\} \ar@{->}[d] &  \{x_{m-2},b_{1},f_{1}\}\\
\{y_{1},c_{1},d_{1}\} & \quad }$$ We already know from the class $\mathfrak{s}_{0}+\mu _{1}$ that the only nontrivial differential of $HF^{\infty }$ in this class is $\partial ^{\infty }[\{x_{m},c_{1},e_{1}\},i]=[\{y_{1},c_{1},d_{1}\},i]$. It follows that $\partial ^{+}[\{x_{m},c_{1},e_{1}\},i]=[\{y_{1},c_{1},d_{1}\},i]$ and also $\partial ^{+}[\{x_{m-2},b_{1},f_{2}\},i]=\partial 