The present paper deals with the resolution of the time-dependent neutron transport equation that is involved in the field of nuclear safety studies. Through the presentation of the newly implemented kinetic module in the MINARET solver [24] (developed at CEA in the framework of the APOLLO3\registered $ $ project), we aim first of all at presenting a brief and comprehensive overview of the most widespread resolution techniques employed nowadays in neutron transport industrial codes. Given that the main obstacle in the use of this type of accurate solver on a regular basis relies in the long computing times, MINARET has been used in the present work as a support to rigorously quantify the efficiency of the most common sequential and parallel acceleration techniques that are currently used in this field. An important part of the paper will be devoted to study the performances of an acceleration method that has never been considered before in the resolution of this equation, which is the parallelization of the time variable. In this regard, the parareal in time algorithm (a domain decomposition method for the time variable, [20]) has been implemented to explore its potentialities in this particular application.