There is a construction of a global affine flag variety over $\mathbb{A}^1$ (or another curve) $Fl_{\mathbb{A}_1}$ such that each fiber above $\epsilon \neq 0$ is isomorphic to a direct product of the affine Grassmannian $Gr$ with the ordinary flag variety $G/B$, $Gr \times G/B$. The fiber above $\epsilon = 0$ is the affine flag variety $Fl$. This first appeared in Gaitsgory's paper 'Construction of central elements in the affine Hecke algebra via nearby cycles' http://arxiv.org/abs/math/9912074

If we have some projective varieties in $Gr \times G/B$, how do we find out more about their images in the affine flag variety $Fl$, as $\epsilon \rightarrow 0$? More precisely in page 5, section 1.2.3 of the paper above, there is this example where for $G = GL_2(\mathbb{C})$, a family of $\mathbb{P}^1 \subset Gr$ degenerates to two copies of $\mathbb{P}^1$ glued at a point, in the affine flag variety $Fl$ for $GL_2(\mathbb{C})$.

How do we verify this? Could we calculate things like this by some concrete methods?

There is a construction of a global affine flag variety over $\mathbb{A}^1$ (or another curve) $Fl_{\mathbb{A}_1}$ such that each fiber above $\epsilon \neq 0$ is isomorphic to a direct product of the affine Grassmannian $Gr$ with the ordinary flag variety $G/B$, $Gr \times G/B$. The fiber above $\epsilon = 0$ is the affine flag variety $Fl$. This first appeared in Gaitsgory's paper 'Construction of central elements in the affine Hecke algebra via nearby cycles' http://arxiv.org/abs/math/9912074

If we have some projective varieties in $Gr \times G/B$, how do we find out more about their images in the affine flag variety $Fl$, as $\epsilon \rightarrow 0$? More precisely in page 5, section 1.2.3 of the paper above, there is this example where for $G = GL_2$, a family of $\mathbb{P}^1 \subset Gr$ degenerates to two copies of $\mathbb{P}^1$ glued at a point, in the affine flag variety $Fl$ for $GL_2$.

How do we verify this? Could we calculate things like this by some concrete methods?