  Non-Markovian dynamics are characterized by information backflows, where the
evolving open quantum system retrieves part of the information previously lost
in the environment. Hence, the very definition of non-Markovianity implies an
initial time interval when the evolution is noisy, otherwise no backflow could
take place. We identify two types of initial noise, where the first has the
only effect of degrading the information content of the system, while the
latter is essential for the appearance of non-Markovian phenomena. Therefore,
all non-Markovian evolutions can be divided into two classes: noisy
non-Markovian (NNM), showing both types of noise, and pure non-Markovian (PNM),
implementing solely essential noise. We make this distinction through a timing
analysis of fundamental non-Markovian features. First, we prove that all NNM
dynamics can be simulated through a Markovian pre-processing of a PNM core. We
quantify the gains in terms of information backflows and non-Markovianity
measures provided by PNM evolutions. Similarly, we study how the entanglement
breaking property behaves in this framework and we discuss a technique to
activate correlation backflows. Finally, we show the applicability of our
results through the study of several well-know dynamical models.
