A sequence of objects $(f_{0},\rho_{0}),...,(f_{k},\rho_{k})$ is called transversal if for any $m\geq 1$ and any binary tree $T$ with $m+1$ tails, an arbitrary subsequence $(f_{i_{0}},...,f_{i_{m}}),i_{0}<...<i_{m}$ is $T$-transversal.