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We study the 3D axis of rotation (3D spin) of 77 H  i galaxies from the MIGHTEE-H  i Early Science observations, and its relation to the filaments of the cosmic web. For this H  i -selected sample, the alignment between the spin axis and the closest filament (|cos ψ|) is higher for galaxies closer to the filaments, with 〈|cos ψ|〉 = 0.66 ± 0.04 for galaxies <5 Mpc from their closest filament compared to 〈|cos ψ|〉 = 0.37 ± 0.08 for galaxies at 5 < d < 10 Mpc. We find that galaxies with a low H  i -to-stellar mass ratio (log10(M H  i / M ⋆) < 0.11) are more aligned with their closest filaments, with 〈|cos ψ|〉 = 0.58 ± 0.04; whilst galaxies with (log10(M H  i / M ⋆) > 0.11) tend to be mis-aligned, with 〈|cos ψ|〉 = 0.44 ± 0.04. We find tentative evidence that the spin axis of H  i -selected galaxies tend to be aligned with associated filaments (d < 10 Mpc), but this depends on the gas fractions. Galaxies that have accumulated more stellar mass compared to their gas mass tend towards stronger alignment. Our results suggest that those galaxies that have accrued high gas fraction with respect to their stellar mass may have had their spin axis alignment with the filament disrupted by a recent gas-rich merger, whereas the spin vector for those galaxies in which the neutral gas has not been strongly replenished through a recent merger tend to orientate towards alignment with the filament. We also investigate the spin transition between galaxies with a high H  i content and a low H  i content at a threshold of |$M_{\rm{H\,{\small {I}}}}\approx 10^{9.5} \mathrm{ M}_{\odot }$| found in simulations; however, we find no evidence for such a transition with the current data. [ABSTRACT FROM AUTHOR]