We say that a sequence $(f_{0},\dots,f_{k}),\,k\geq 2$ is $T$-transversal for a given tree $T$, if for any sequence of intersection points $(x_{0},\dots,x_{k})$ such that

$$\sum_{i=0}^{k-1}ind(x_{i})-ind(x_{k})\leq k-2$$

the collection of submanifolds $\bigl((Z_{v_{m}})_{0\leq m\leq k},(Z_{e})_{e\in E_{i}(T)}\bigr)$ is transversal in $Y(T)$ (i.e. intersection of any subcollection is transversal). For $k=1$, we say that $(f_{0},f_{1})$ is $T$-transversal (there is only one tree $T$ in this case) if $f_{0}-f_{1}$ is a Morse function, satisfying the Morse-Smale transversality condition.