$[\{x_{1},b_{n-2},f_{1}\},i]$ for $i\geq 0$.

**Class $\mathfrak{s}_{0}-\mu _{2}$** $$\xymatrix{ \{x_{1},c_{1},e_{1}\} \ar@{->}[d]& \quad \\
\{u_{2},a_{2},e_{1}\} & \{x_{m-1},b_{2},f_{2}\} \ar@{.>}[d]\\
\quad & \{x_{m-1},b_{2},f_{1}\}}$$

[1]{} & {x\_[1]{},c\_[1]{},e\_[1]{}}{u\_[2]{},a\_[2]{},e\_[1]{}}D\_[2]{} ,\
& {x\_[1]{},c\_[1]{},e\_[1]{}}{x\_[m-1]{},b\_[2]{},f\_[2]{}}D\_[2]{}+D\_[3]{}+D\_[6]{}+D\_[7]{}+D\_[9]{}-D\_[10]{}+D\_[12]{}-\
& -D\_[13]{}-D\_[14]{}-D\_[15]{}+B\_[1]{}+…+B\_[n-3]{} ,\
& {u\_[2]{},a\_[2]{},e\_[1]{}}{x\_[1]{},c\_[1]{},e\_[1]{}}=D\_[1]{}+D\_[5]{}+D\_[7]{}+D\_[8]{}+D\_[10]{}+2D\_[13]{}+D\_[15]{}+\
& +A\_[1]{}+…+A\_[m-3]{}, ++2\
& {u\_[2]{},a\_[2]{},e\_[1]{}}{x\_[m-1]{},b\_[2]{},f\_[1]{}}D\_[3]{}+D\_[6]{}+D\_[7]{}+D\_[9]{}-D\_[10]{}+D\_[12]{}-D\_[14]{}-\
& -D\_[15]{}+B\_[1]{}+…+B\_[n-3]{} ,\
& {x\_[m-1]{},b\_[2]{},f\_[2]{}}{x\_[1]{},c\_[1]{},e\_[1]{}}=D\_[1]{}+D\_[4]{}+D\_[5]{}+D\_[8]{}+2D\_[10]{}+D\_[11]{}+2D\_[13]{}+\
& +2D\_[14]{}+2D\_[15]{}+D\_[16]{}+A\_[1]{}+…+A\_[m-3]{}, ++2\
& {x\_[m-1]{},b\_[2]{},f\_[2]{}}{x\_[m-1]{},b\_[2]{},f\_[1]{}}D\_[13]{}D\_[13]{}+\
& {x\_[m-1]{},b\_[2]{},f\_[1]{}}{u\_[2]{},a\_[2]{},e\_[1]{}}=D\_[1]{}+D\_[2]{}+D\_[4]{}+D\_[5]{}+D\_[8]{}+2D\_[10]{}+D\_[11]{}+\
& +D\_[13]{}+2D\_[14]{}+2D\_[15]{}+D\_[16]{}+A\_[1]{}+…+A\_[m-3]{}+\
& {x\_[m-1]{},b\_[2]{},f\_[1]{}}{x\_[m-1]{},b\_[2]{},f\_[2]{}}=D\_[1]{}+D\_[2]{}+D\_[5]{}+D\_[7]{}+D\_[8]{}+D\_[10]{}+D\_[13]{}+\
& +D\_[15]{}+A\_[1]{}+…+A\_[m-3]{}+

By an analogous reasoning as in the class $\mathfrak{s}_{0}+\mu _{1}$ we conclude that $HF^{+}(Y,\mathfrak{s}_{0}-\mu _{2})\cong {\mathcal{T}^{+}}\oplus {\mathcal{T}^{+}}$ is freely generated by the elements $[\{x_{m-1},b_{2},f_{2}\},i]$ and $[\{x_{m-1},b_{2},f_{1}\},i]$ for $i\geq 0$.

**Class $\mathfrak{s}_{0}-\mu _{1}$** $$\xymatrix{\{x_{m},c_{2},e_{2}\} \ar@{->}[d] & \quad \\
\{u_{1},a_{2},e_{2}\} & \{x_{2},b_{n-1},f_{2}\} \ar@{.>}[d]\\
\quad & \{x_{2},b_{n-1},f_{1}\}}$$

[1]{} & {x\_[m]{},c\_[2]{},e\_[2]{}}{u\_[1]{},a\_[2]{},e\_[2]{}}D\_[15]{} ,\
& {x\_[m]{},c\_[2]{},e\_[2]{}}{x\_[2]{},b\_[n-1]{},f\_[2]{}}-D\_[2]{}-D\_[3]{}-D\_[4]{}-D\_[6]{}+D\_[8]{}+D\_[10]{}+D\_[15]{}+A\_[1]{}+\
& +A\_[2]{}+…+A\_[m-3]{} ,\
& {u\_[1]{},a\_[2]{},e\_[2]{}}{x\_[m]{},c\_[2]{},e\_[2]{}}=D\_[1]{}+D\_[2]{}+D\_[5]{}+D\_[7]{}+D\_[8]{}+D\_[10]{}+2D\_[13]{}+A\_[1]{}+\
& +A\_[2]{}+…+A\_[m-3]{}, ++2\
& {u\_[1]{},a\_[2]{},e\_[2]{}}{x\_[2]{},b\_[n-1]{},f\_[1]{}}-D\_[2]{}-D\_[3]{}-D\_[4]{}-D\_[6]{}+D\_[8]{}+D\_[10]{}+D\_[13]{}+A\_[1]{}+\
& +A\_[2]{}+…+A\_[m-3]{} ,\
& {x\_[2]{},b\_[n-1]{},f\_[2]{}}{x\_[m]{},c\_[2]{},e\_[2]{}}=D\_[1]{}+2D\_[2]{}+D\_[3]{}+D\_[4]{}+D\_[5]{}+D\_[6]{}+D\_[7]{}+2D\_[13]{},\
& ++2\
& {x\_[2]{},b\_[n-1]{},f\_[2]{}}{x\_[2]{},b\_[n-1]{},f\_[1]{}}D\_[13]{}D\_[13]{}+\
& {x\_[2]{},b\_[n-1]{},f\_[1]{}}{u\_[1]{},a\_[2]{},e\_[2]{}}D\_[1]{}+2D\_[2]{}+2D\_[3]{}+2D\_[4]{}+D\_[5]{}+2D\_[6]{}+D\_[7]{}+D\_[9]{}+\
& +D\_[11]{}+D\_[12]{}+D\_[14]{}+D\_[15]{}+D\_[16]{}+B\_[1]{}+…+B\_[n-3]{}\
& {x\_[2]{},b\_[n-1]{},f\_[1]{}}{x\_[2]{},b\_[n-1]{},f\_[2]{}}=D\_[1]{}+D\_[2]{}+D\_[5]{}+D\_[7]{}+D\_[8]{}+D\_[10]{}+D\_[13]{}+\
& +D\_[15]{}+A\_[1]{}+…+A\_[m-3]{}+

Again we use an analogous reasoning as in the class $\mathfrak{s}_{0}+\mu _{1}$ to obtain $$HF^{+}(Y,\mathfrak{s}_{0}-\mu _{1})\cong {\mathcal{T}^{+}}\oplus {\mathcal{T}^{+}}\;,$$ freely generated by the elements $[\{x_{2},b_{n-1},f_{2}\},i]$ and $[\{x_{2},b_{n-1},f_{1}\},i]$ for $i\geq 0$.

In the following calculations, we apply the change of basepoint formula using [@OS1 Lemma 2.19]:

\[lemaz\] Let $(\Sigma ,(\alpha _{1},\ldots ,\alpha _{g}),(\beta _{1},\ldots ,\beta _{g}),z_{1})$ be a Heegaard diagram. Denote by $z_{2}\in \Sigma -\alpha _{1}-\ldots -\alpha _{g}-\beta _{1}-\ldots -\beta _{g}$ a 