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 $\pi_N$.