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We present a study of the three-dimensional (3D) distribution of interstellar dust derived from stellar extinction observations toward the Taurus molecular cloud (MC) and its relation with the neutral atomic hydrogen (HI) emission at 21 cm wavelength and the carbon monoxide $^{12}$CO and $^{13}$CO emission in the $J=1\rightarrow0$ transition. We used the histogram of oriented gradients (HOG) method to match the morphology in a 3D reconstruction of the dust density (3D dust) and the distribution of the gas tracers' emission. The result of the HOG analysis is a map of the relationship between the distances and radial velocities. The HOG comparison between the 3D dust and the HI emission indicates a morphological match at the distance of Taurus but an anti-correlation between the dust density and the HI emission, which uncovers a significant amount of cold HI within the Taurus MC. The HOG between the 3D dust and $^{12}$CO reveals a pattern in radial velocities and distances that is consistent with converging motions of the gas in the Taurus MC, with the near side of the cloud moving at higher velocities and the far side moving at lower velocities. This convergence of flows is likely triggered by the large-scale gas compression caused by the interaction of the Local Bubble and the Per-Tau shell, with Taurus lying at the intersection of the two bubble surfaces.