  This study attempts to establish a link between the reasonably well known
nature of the progenitor of SN2011fe and its surrounding environment. This is
done with the aim of enabling the identification of similar systems in the vast
majority of the cases, when distance and epoch of discovery do not allow a
direct approach. To study the circumstellar environment of SN2011fe we have
obtained high-resolution spectroscopy of SN2011fe on 12 epochs, from 8 to 86
days after the estimated date of explosion, targeting in particular at the time
evolution of CaII and NaI. Three main absorption systems are identified from
CaII and NaI, one associated to the Milky Way, one probably arising within a
high-velocity cloud, and one most likely associated to the halo of M101. The
Galactic and host galaxy reddening, deduced from the integrated equivalent
widths (EW) of the NaI lines are E(B-V)=0.011+/-0.002 and E(B-V)=0.014+/-0.002
mag, respectively. The host galaxy absorption is dominated by a component
detected at the same velocity measured from the 21-cm HI line at the projected
SN position (~180 km/s). During the ~3 months covered by our observations, its
EW changed by 15.6+/-6.5 mA. This small variation is shown to be compatible
with the geometric effects produced by therapid SN photosphere expansion
coupled to the patchy fractal structure of the ISM. The observed behavior is
fully consistent with ISM properties similar to those derived for our own
Galaxy, with evidences for structures on scales <100 AU. SN2011fe appears to be
surrounded by a "clean" environment. The lack of blue-shifted, time-variant
absorption features is fully consistent with the progenitor being a binary
system with a main-sequence, or even another degenerate star.
