  In this contribution, the transitivity property of commutative first-order
linear time-varying systems is investigated with and without initial
conditions. It is proven that transitivity property of first-order systems
holds with and without initial conditions. On the base of impulse response
function, transitivity of commutation property is formulated for any triplet of
commutative linear time-varying relaxed systems. Transitivity proves are given
for some special combinations of first and second-order linear time-varying
systems which are initially relaxed.
