Definition 2

The family $x$ is said to be completely transverse for $M$ if one has $H_i(x,M)=0$ for $i>0$.

If $I$ is finite, it amounts to the same thing (X, p. 150) to say that one has $H^i(x,M)=0$ for $i<\operatorname{Card}(I)$.

The following proposition makes it possible to give examples of completely transverse families.