  We investigate the Landau-Zener transition in two- and three- level systems
subject to a classical Gaussian noise. Two complementary limits of the noise
being fast and slow compared to characteristic Landau-Zener tunnel times are
discussed. The analytical solution of a density matrix (Bloch) equation is
given for a long time asymptotic of transition probability. It is demonstrated
that the transition probability induced/assisted by the fast noise can be
obtained through a procedure of {\it Bloch's equation averaging} with further
reduction it to a master equation. In contrast to the case of fast noise, the
transition probability for LZ transition induced/assisted by the slow classical
noise can be obtained by averaging a {\it solution} of Bloch's equation over
the noise realization. As a result, the transition probability is described by
the activation Arrhenius law. The approximate solution of the Bloch's equation
at finite times is written in terms of Fresnel's integrals and interpreted in
terms of interference pattern. We discuss consequences of a local isomorphism
between SU(2) and SO(3) groups and connections between Schr\"odinger and Bloch
descriptions of spin dynamics. Based on this isomorphism we establish the
relations between S=1/2 and S=1 transition probabilities influenced by the
noise. A possibility to use the slow noise as a probe for tunnel time is
discussed.
