Gaia stellar measurements are currently revolutionizing our knowledge of the evolutionary history of the Milky Way. 3D maps of the interstellar dust provide complementary information and are a tool for a wide range of uses. We built 3D maps of the dust in the Local arm and surrounding regions. To do so, Gaia DR2 photometric data were combined with 2MASS measurements to derive extinction toward stars that possess accurate photometry and relative uncertainties on DR2 parallaxes smaller than 20%. We applied a new hierarchical inversion algorithm to the individual extinctions that is adapted to large datasets and to an inhomogeneous target distribution. Each step associates regularized Bayesian inversions in all radial directions and a subseque...