We present the first cross-identifications of sources in the near-infrared DENIS survey and in the micro-lensing EROS survey in a field of about 0.5 square degrees around the optical center (OC) of the Large Magellanic Cloud. We analyze the photometric history of these stars in the EROS data base and obtain light-curves for about 800 variables. Most of the stars are long period variables (Miras and Semi-Regulars); a few Cepheids are also present. We also present new spectroscopic data on 126 asymptotic giant branch stars in the OC field, 30 previously known and 96 newly discovered by the DENIS survey. The visible spectra are used to assign a carbon- (C-) or oxygen-rich (O-rich) nature to the observed stars on the basis of the presence of molecular bands of TiO, VO, CN, C_2_. For the remaining of the stars we used the (J-K_S_) color to determine whether they are O-rich or C-rich. Plotting Log(period) versus K_S_ we find three very distinct period-luminosity relations, mainly populated by Semi-Regular stars of type a (SRa), b (SRb) and Mira variables. Carbon-rich stars occupy mostly the upper part of these relations. We find that 65% of the asymptotic giant branch population are long period variables (LPVs).