We studied the global and local M-Z relation based on the first data available from the CALIFA survey (150 galaxies). This survey provides integral field spectroscopy of the complete optical extent of each galaxy (up to 2-3 effective radii), with a resolution high enough to separate individual H II regions and/or aggregations. About 3000 individual HII regions have been detected. The spectra cover the wavelength range between [OII]3727 and [SII]6731, with a sufficient signal-to-noise ratio to derive the oxygen abundance and star-formation rate associated with each region. In addition, we computed the integrated and spatially resolved stellar masses (and surface densities) based on SDSS photometric data. We explore the relations between the stellar mass, oxygen abundance and star-formation rate using this dataset. We derive a tight relation between the integrated stellar mass and the gas-phase abundance, with a dispersion lower than the one already reported in the literature (σΔlog(O/H) = 0.07 dex). Indeed, this dispersion is only slightly higher than the typical error derived for our oxygen abundances. However, we found no secondary relation with the star-formation rate other than the one induced by the primary relation of this quantity with the stellar mass. The analysis for our sample of ~3000 individual HII regions confirms (i) a local mass-metallicity relation and (ii) the lack of a secondary relation with the star-formation rate. The same analysis was performed with similar results for the specific star-formation rate. Our results agree with the scenario in which gas recycling in galaxies, both locally and globally, is much faster than other typical timescales, such like that of gas accretion by inflow and/or metal loss due to outflows. In essence, late-type/disk-dominated galaxies seem to be in a quasi-steady situation, with a behavior similar to the one expected from an instantaneous recycling/closed-box model. Table 1 and Appendix A are available in electronic form at http://www.aanda.org.