We examine whether there are deviations of the local central oxygen abundancesin spiral galaxies from the general metallicity gradients. We compare thevalues of the central intersect oxygen abundances estimated from themetallicity gradient based on the integral field unit (IFU) spectroscopy fromthe Mapping Nearby Galaxies at the Apache Point Observatory (MaNGA) survey andthe local central oxygen abundances obtained from the single-fibre observations from the Sloan Digital Sky Survey (SDSS). Special attention is placed ongalaxies with recent and currently ongoing central starbursts (cSB galaxies).We selected a sample of 30 cSB galaxies from our total sample of 381 MaNGAgalaxies, using the decrease in the Dn4000 index (a stellar age indicator) inthe circumnuclear region as the selection criterion. We found that the local central oxygen abundances follow the general metallicity gradients in thegalaxies well and agree with the central intersect abundances withinuncertainties of the central abundances determinations. Starbursts in thecentres of cSB galaxies do not produce noticeable oxygen enrichments. Thecentral starbursts imply that an appreciable amount of gas is present at thecentres of cSB galaxies. The gas at the centre of galaxy can serve not only asa raw material for the star formation, but also as a fuel for the activity ofthe galactic nucleus (AGN). We found that the AGN is the main source of theionising radiation at the centres of six cSB galaxies in our sample.