Let $S$ be an Enriques surface, i.e. a quotient of a K3 surface by a free involution. Enriques surfaces arise as elliptic fibrations $S\rightarrow \mathbb{P}^1$ with 12 singular fibers and 2 double points. 



> 
> **Claim** There exist elliptic surfaces $S\_1, S\_2$ such that 
>  we can degenerate the elliptic fibration $S\rightarrow \mathbb{P}^1$ to get 
>  $$
> S\_1 \cup\_E S\_2 \rightarrow \mathbb{P}^1
> $$
>  wherethe intersection $E$ is a common elliptic fiber. 
> 
> 
> 


**Question**
How can I prove this claim? 


More precisely, the elliptic surfaces $S\_1, S\_2$ are obtained as follows:


Let $E\times \mathbb{P}^1$ be the product of elliptic curve and a projective line. Let $t$ denote the translation by a 2-torsion point on $E$, and let $\iota$ be an involution of $\mathbb{P}^1$. Then $(t\_2,\iota)$ is a fixed point free involution on $E\times \mathbb{P}^1$, and we define
$$
S\_1:=(E\times \mathbb{P}^1)/\langle (t\_2,\iota) \rangle. 
$$
By projecting right, $S\_1\rightarrow \mathbb{P}^1/\langle \iota \rangle$ is an elliptic fibration with no singular fibers and 2 double fibers. 


Let $S\_2$ be the blow-up of $\mathbb{P}^2$ in 9 points. $S\_2$ admits an elliptic fibration 
$S\_2\rightarrow \mathbb{P}^1$ with 12 singular fibers and no double fibers.



A question on existence of degeneration of Enriques surface. 
The surface $S\_1$ is rational and the surface is an elliptic ruled surface (induced by the projection $E\times \mathbb{P}^1\to E$). The glued surface is a standard Type II degeneration of Enriques surfaces (an elliptic ruled chain) classified by Vic. Kulikov and D. Morrison. I believe that the general member of the deformation is the Enriques surface obtained by the logarithmic transformation at two isomorphic nonsingular fibers corresponding to the choice of the same 2-torsion on each fiber. But this has to be checked. 


