Photometry in B, V (down to V ~ 26 mag) is presented for two 23 x 23 fields of the Andromeda galaxy (M31) that were observed with the blue channel camera of the Large Binocular Telescope during the Science Demonstration Time. Each field covers an area of about 5.1kpc x 5.1kpc at the distance of M31 ((m-M)o ~ 24.4 mag), sampling, respectively, a northeast region close to the M31 giant stream (field S2), and an eastern portion of the halo in the direction of the galaxy minor axis (field H1). The stream field spans a region that includes Andromedas disk and the giant stream, and this is reflected in the complexity of the color magnitude diagram of the field. One corner of the halo field also includes a portion of the giant stream. Even though these demonstration time data were obtained under non-optimal observing conditions the B photometry, acquired in time-series mode, allowed us to identify 274 variable stars (among which 96 are bona fide and 31 are candidate RR Lyrae stars, 71 are Cepheids, and 16 are binary systems) by applying the image subtraction technique to selected portions of the observed fields. Differential flux light curves were obtained for the vast majority of these variables. Our sample includes mainly pulsating stars which populate the instability strip from the Classical Cepheids down to the RR Lyrae stars, thus tracing the different stellar generations in these regions of M31 down to the horizontal branch of the oldest (t ~ 10 Gyr) component.