Existence problem and deformation of compact Clifford-Klein forms

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At first, I had planed to calculate deformation spaces of Clifford-Klein forms. However, I found that such deformation spaces are non-Hausdorff in many cases, and it is not easy to get an intuition of the deformation space.In order to understand such non-Hausdorff spaces, I have introduced a method topological blow-up'. This method is similar to the blow-up for algebraic varieties. Applying this method for a non-Hausdorff space, we obtain a Hausdorff space. This Hausdorff space has much information about the topology of the original non-Hausdorff space. Especially, if we apply it for deformation spaces of Clifford-Klein forms, we can obtain complete information on the topology of the deformation space from the blow-upped spaces.