  Context. The EROS-2 survey has produced a database of millions of time series
from stars monitored for more than six years, allowing to classify some of
their sources into different variable star types. Among these, Long Period
Variables (LPVs), known to follow sequences in the period-luminosity diagram,
include long secondary period variables whose variability origin is still a
matter of debate.
  Aims.We use the 856 864 variable stars available from the Large Magellanic
Cloud (LMC) in the EROS-2 database to detect, classify and characterize LPVs.
  Methods. Our method to extract LPVs is based on the statistical Abbe test. It
investigates the regularity of the light curve with respect to the survey
duration in order to extract candidates with long-term variability. The period
search is done by Deeming, Lomb-Scargle and generalized Lomb-Scargle methods,
combined with Fourier series fit. Color-magnitude, period-magnitude and
period-amplitude diagrams are used to characterize our candidates.
  Results. We present a catalog of 43 551 LPV candidates for the Large
Magellanic Cloud. For each of them, we provide up to five periods, mean
magnitude in EROS-2, 2MASS and Spitzer bands, BE-RE color, RE amplitude and
spectral type.We use infrared data to make the distinction between RGB, O-rich,
C-rich and extreme AGB stars. Properties of our LPV candidates are investigated
by analyzing period-luminosity and period-amplitude diagrams.
