A Covenant is a contract. One party does his part and the other party does their part. In this case Man repents and believes and God regenerates and forgives. The condition precedent to God's act of regeneration is the requirement that man must first repent and believe.
Since man is seperated from God by sin and since God, being holy, cannot tolerate or accept sin in his presence, then it would be impossible for man to enter into God's presence or to have fellowship with God unless and until his sins have been forgiven. Forgiveness comes only after repentance and thus the indwelling of the Holy Spirit cannot occur until God has first sanctified his temple. Regeneration occurs when God indwells us. Since God cannot indwell us while we are sinners, we must first repent and believe before the transformation can occur.
Calvinism assumes that it is possible for God to indwell a sinner who has not yet repented. Calvinism thus makes the cross irrelevant.