Let $(B,\Delta,\mathscr{A})$ be a given simple affine 3-manifold with singularities. Then we have the following

• (i)

  if $J\subseteq\Delta_{g}$ is an edge of $\Delta$, then there is a generic-singular fibration $\mathcal{F}$, with affine base $(B^{\prime},\Delta^{\prime},\mathscr{A}^{\prime})$ and neighborhood $U\subseteq B$ of $J$ such that there exists an integral affine isomorphism $(B^{\prime},\Delta^{\prime},\mathscr{A}^{\prime})\cong(U,J,\mathscr{A})$ inducing a symplectic conjugation $X(B^{\prime}_{0},\mathscr{A}^{\prime})\cong X(U-J,\mathscr{A})$;

• (ii)

  if $p\in\Delta_{d}$ is a positive vertex of $\Delta$, then there is positive fibration $\mathcal{F}$ with base $(B^{\prime},\Delta^{\prime},\mathscr{A}^{\prime})$ and a neighborhood $U\subseteq B$ of $p$ such that there exists an integral affine isomorphism $(B^{\prime},\Delta^{\prime},\mathscr{A}^{\prime})\cong(U,U\cap\Delta,\mathscr{A})$ inducing a symplectic conjugation $X(B^{\prime}_{0},\mathscr{A}^{\prime})\cong X(U-(U\cap\Delta),\mathscr{A})$.

Moreover, using the symplectic conjugations in (i) and (ii), we can symplectically glue the germ of $\mathcal{F}$ into $X(B_{0},\mathscr{A})$.