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Monte Carlo methods have been used for nuclear applications since the beginning of scientific computing. Decades of method refinements now allow to perform simulations of steady-state fissile systems with quite accurate results and relatively accessible computation time. Timedependent calculations such as reactivity insertion accident simulations on the other hand still present issues. Indeed, reaching a sufficient accuracy implies high computational costs which prohibit industrial use of time-dependent Monte Carlo simulations. Dynamic calculations which include thermal feedback effects using coupled calculation schemes might especially suffer from high statistical fluctuations due to the non-linearity of multiphysics solvers. To address this issue, with the aim of reducing variance in Monte Carlo transient neutronics simulations, this article proposes a strategy based on adaptive sampling of neutron histories. The method which is proposed here is adapted from the Adaptive Multilevel Splitting method for particle transport and can make use of an importance map provided by the user. A first test of the method was conducted on a 2-dimensional 3x3 UOX assembly cluster to produce detailed and spatially integrated power distributions over time. Increases of the figure of merit up to a factor 30 were observed for detailed and spatially integrated results at the end of the neutronics transient. Such improvements of the figure of merit could eventually prove to be efficient to reduce potential amplifications of statistical fluctuations due to non-linearity of other multiphysics solvers with affordable calculation costs.