An analysis of the stability of the spindle transform, introduced in (Three dimensional Compton scattering tomography arXiv:1704.03378 [math.FA]), is presented. We do this via a microlocal approach and show that the normal operator for the spindle transform is a type of paired Lagrangian operator with blowdown--blowdown singularities analogous to that of a limited data synthetic aperture radar (SAR) problem studied by Felea et. al. (Microlocal analysis of SAR imaging of a dynamic reflectivity function SIAM 2013). We find that the normal operator for the spindle transform belongs to a class of distibutions $I^{p,l}(Deltacupwidetilde{Delta},Lambda)$ studied by Felea and Marhuenda (Microlocal analysis of SAR imaging of a dynamic reflectivity function SIAM 2013 and Microlocal analysis of some isospectral deformations Trans. Amer. Math.), where $widetilde{Delta}$ is reflection through the origin, and $Lambda$ is associated to a rotation artefact. Later, we derive a filter to reduce the strength of the image artefact and show that it is of convolution type. We also provide simulated reconstructions to show the artefacts produced by $Lambda$ and show how the filter we derived can be applied to reduce the strength of the artefact.
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