  Kochol (2021) gave a new expansion formula for the Tutte polynomial of a
matroid using the notion of \emph{compatible sets}, and asked how this
expansion relates to the internal-external activities formula. Here, we provide
an answer, which is obtained as a special case of a generalized version of the
expansion formula to Las Vergnas's trivariate Tutte polynomials of matroid
perspectives. The same generalization to matroid perspectives and bijection
with activities have been independently proven by Kochol (2022 and 2023) in
parallel with this work, but using different methods. Kochol proves both
results recursively using the contraction-deletion relations, whereas we give a
more direct proof of the bijection and use that to deduce the compatible sets
expansion formula from Las Vergnas's activities expansion.
