What does the "blanket" represent in the play's final scene?

In the play's final scene, the blanket that Eddie offers Jess (which used to belong to Ani) represents the warmth of connection that Eddie found with Ani that he hopes to find with Jess. Again, the point is not made to suggest that Eddie wants the same kind of intimate, marriage (and marriage-like) relationship he had with Ani, but rather that he is simply seeking the same kind of honest, caring connection with Jess that he had with Ani.