In "The Crucible" what changes can you see in the relationships between men and women throughout the play?

To answer this, it is a good idea to look at John's relationships with two different women; one is Elizabeth and the other is Abigail Williams.  At the beginning of the play, Elizabeth and John are civil at best; the maintain a strained and very awkward relationship.  In act two, Miller takes some time to describe Elizabeth trying to please John with the dinner, and John trying to please Elizabeth by asking about the cow and telling her that the food is good.  But soon, when Elizabeth starts pressuing him to go into town to tell them what Abby had told him, things go bad.  Elizabeth's resentment of the affair and lingering bitterness comes out, and John's resentment of her grudge and defensiveness about his mistakes comes out.  They end up fighting.

But later, in act four, as they meet before John's death, things have changed.  John has expended great effort to rescue Liz from being in jail, and they have both spent some sobering time in prison.  So when they meet again, the defenses and pride has dropped; they speak honestly.  John asks for forgiveness, she asks for forgiveness for being cold, he asks her advice, she cries.  It is emotionally intimate enough to prompt John to declare, "I want my life."  So, the Proctors went from arguing, resentful and mistrusting to honest, loving and vulnerable in each other's presence.

With Abby, John and her were on friendly terms at the beginning; in fact, Abby was very forward and desiring their intimacy to continue; John was stalwart but kind.  He showed her a bit of joking familiarity and even admitted to having hovered outside of her window on occasion.  But by the time act three rolls around, John is so angry with Abby (she is responsible for his wife being imprisoned, after all) that he rages to the entire court, not caring who hears, calling her a "whore".  He rejects her every attempt to win him over, threatens her, and reveals her for who she really is.  So, their relationship went from an intimate affair to pure and bitter hatred.

I hope that helps a bit; good luck!