Their baby is a direct product of their strong sexual desire for one another. They may not have the same upbringing, but they share the same passion. That passion produced a baby and shows Blanche that they have a strong relationship. The baby is the new common thread with Stella and Stanley, whereas Belle Reve was the old common thread between Stella and Blanche. She pretends to make it pure and innocent.
Sparks begin to fly between the two, and sexuality is at the core of the relationship.
However, Blanche and Mitch do not see one another as sexually as Stella and Stanley see each other. They want companionship more than passion. Stanley is screaming for his love, his baby, his Stella. She is angry with him for hitting her, but she returns to him. Her slow walk down the staircase and into his arms is full of sexual tension.