  We have studied Markov processes on denumerable state space and continuous
time. We found that all these processes are connected via gauge
transformations. We have used this result before as a method for resolution of
equations, included the case where the sample space is time dependent in a
previous work \textit{Phys. Rev. E} \textbf{90}, 022125 (2014). We found a
general solution through a dilation of the state space, although the prior
probability distribution of the states defined in this new space takes smaller
values with respect to the one in the initial problem. The gauge (local) group
of dilations modifies the distribution on the dilated space to restore the
original process. In this work we show how Markov process in general could be
linked via gauge (local) transformations and we present some illustrative
examples for this results.
