  We study the tunneling through an arbitrary number of finite rectangular
opaque barriers and generalize earlier results by showing that the total
tunneling phase time depends neither on the barrier thickness nor on the
inter-barrier separation. We also predict two novel peculiar features of the
system considered, namely the independence of the transit time (for non
resonant tunneling) and the resonant frequency on the number of barriers
crossed, which can be directly tested in photonic experiments. A thorough
analysis of the role played by inter-barrier multiple reflections and a
physical interpretation of the results obtained is reported, showing that
multibarrier tunneling is a highly non-local phenomenon.
