$\Phi_{F,H}$ simultaneously; the fibrations $\mathcal F$, $\mathcal G$ and $\mathcal H$ are associated to pencil submersions $\mathcal F_0$, $\mathcal G_0$ and $\mathcal H_0$. Let us call $B= tang(\mathcal F,\mathcal H)\cap C$ and $B_0= tang(\mathcal F_0,\mathcal H_0)\cap C_0$. We consider two foliations $\mathcal I$ and $\mathcal L$ on $\mathbb P^2$ like before. Remark that $Z(\mathcal{I}, C_0)= Z(\mathcal{L}, C_0)=d$. We will assume: 1) all singularities of $\mathcal I$ and $\mathcal L$ lie outside the set $K= A_0 \cup \phi(A)\cup B_0 \cup \phi(B)$; 2) all curves of tangencies between $\mathcal I$ and $\mathcal L$ cross $C_0$ outside the set $K$. We denote $\mathcal I^*= \Phi_{F,G}^*(\mathcal I)$ and $\mathcal L^*= \Phi_{F,H}^*(\mathcal L)$. We will use again the formulae from [@BRU] to compute numerical invariants associated to tangent lines between two foliations. We have: $$tang(\mathcal I,\mathcal L)\cdot C_0= N_{\mathcal I} \cdot C_0 + N_{\mathcal L}\cdot C_0 + K_{\mathbb P^2}\cdot C_0=2d^2 -d,$$ since $\mathcal I$ and $\mathcal H$ have degree $d-1$ and $K_{\mathbb P^2}\cdot C_0 =-3d$.

Let us call $\mathcal Z_1(\mathcal I^*,C)$ ($\mathcal Z_1(\mathcal L^*,C))$ the set of points where $\Phi_{F,G}$ is not a local biholomorphism (respectively $\Phi_{F,H}$ is not a local biholomorphism). We define $Z_1(\mathcal I^*,C)$ as the sum of all indexes $Z(\mathcal I^*,C,p)$ at 