The early and complete temporal characterization of optical, fast, transient sources requires continuous and multi-band observations over different timescales (hours to months). For timing astronomy, the use of several telescopes to analyze single objects is the usual method, allowing the acquisition of highly sampled light curves. Taking a series of images each night helps to construct an uninterrupted chain of observations with a high cadence and low duty cycle. Speed is paramount, especially at early times in order to capture early features in the light curve that help determine the nature of the observed transients and assess their astrophysical interest. However, the problem of rapidly extracting source properties (temporal and color evolution) with a heterogeneous dataset remains. To address this, we present Muphoten, a general and fast-computation photometric pipeline, suitable for the calibration of transient brightness over multi-telescope and multi-band networks, with the goal of a single photometric time-series. We show the performance of Muphoten with observations of the optical transient SN 2018cow (from 06.2018 to 07.2018), monitored by the GRANDMA network and with the publicly available data of the Liverpool Telescope.