We present absorption line strength maps of a sample of 24 representative early-type spiral galaxies , mostly of type Sa , obtained as part of the SAURON survey of nearby galaxies using our custom-built integral-field spectrograph . Using high-quality spectra , spatially binned to a constant signal-to-noise , we measure several key age , metallicity and abundance ratio sensitive indices from the Lick/IDS system over a contiguous two-dimensional field including bulge and inner disc . We present maps of H \beta , Fe 5015 , and Mg b , for each galaxy . We find that Sa galaxies on the average have slightly smaller Mg b and Fe 5015 line strengths than ellipticals and S0s , and higher H \beta values , but with a much larger scatter . The absorption line maps show that many galaxies contain some younger populations ( \leq 1 Gyr ) , distributed in small or large inner discs , or in circumnuclear star forming rings . In many cases these young stars are formed in circumnuclear mini-starbursts , which are dominating the light in the centres of some of the early-type spirals . These mini-starburst cause a considerable scatter in index-index diagrams such as Mg b – H \beta and Mg b – Fe 5015 , more than is measured for early-type galaxies . We find that the central regions of Sa galaxies display a wide range in ages , even within the galaxies . We find that the central regions of early-type spirals are often dusty , with a good correlation between the presence of young central stellar populations and a significant amount of dust extinction . 50 % of the sample show velocity dispersion drops in their centres . All of the galaxies of our sample lie on or below the Mg b – \sigma relation for elliptical galaxies in the Coma cluster , and above the H \beta absorption line – \sigma relation for elliptical galaxies . If those relations are considered to be relations for the oldest local galaxies we see that our sample of spirals has a considerable scatter in age , with the largest scatter at the lowest \sigma . This is in disagreement with highly inclined samples , in which generally only old stellar populations are found in the central regions . The discrepancy between our sample and highly inclined samples , and the presence of so many stellar velocity dispersion dips , i.e. , so-called \sigma -drops , in these spiral galaxies with large bulges ( type Sa ) can be understood if the central regions of Sa galaxies contain at least 2 components : a thin , disc-like component , often containing recent star formation , and another , elliptical-like component , consisting of old stars and rotating more slowly , dominating the light above the plane . These components together form the photometrically defined bulge , in the same way as the thin and the thick disc co-exist in the solar neighbourhood . In this picture , consistent with the current literature , part of the bulge , the thicker component , formed a very long time ago . Later , stars continued to form in the central regions of the disc , rejuvenating in this way the bulge through dynamical processes . This picture is able to explain in a natural way the heterogeneous stellar populations and star formation characteristics that we are seeing in detailed observations of early-type spiral galaxies .