  The $\pi$-calculus is a process algebra where agents interact by sending
communication links to each other via noiseless communication channels. Taking
into account the reality of noisy channels, an extension of the $\pi$-calculus,
called the $\pi_N$-calculus, has been introduced recently. In this paper, we
present an early transitional semantics of the $\pi_N$-calculus, which is not a
directly translated version of the late semantics of $\pi_N$, and then extend
six kinds of behavioral equivalences consisting of reduction bisimilarity,
barbed bisimilarity, barbed equivalence, barbed congruence, bisimilarity, and
full bisimilarity into the $\pi_N$-calculus. Such behavioral equivalences are
cast in a hierarchy, which is helpful to verify behavioral equivalence of two
agents. In particular, we show that due to the noisy nature of channels, the
coincidence of bisimilarity and barbed equivalence, as well as the coincidence
of full bisimilarity and barbed congruence, in the $\pi$-calculus does not hold
in $\pi_N$.
