The versal deformation of small resolutions of conic bundles over ${\mathbb{P}}^1\times {\mathbb{P}}^1$ with two sections blown down

Twistor spaces are certain compact complex threefolds with an additional real fibre bundle structure. We focus here on twistor spaces over $3\mathbb{C}{\mathbb{P}}^2$. Such spaces are either small resolutions of double solids or they can be described as modifications of conic bundles. The last type is the more special one: they deform into double solids. We give an explicit description of this deformation, in a more general context.