We enter into a blood covenant with Jesus when we are baptized in Jesus name for the remission of sins. The Bible compares this covenant with the covenant of circumcision. 

"In whom also ye are circumcised with the circumcision made without hands, in putting off the body of the sins of the flesh by the circumcision of Christ: buried with him in baptism, wherein also ye are risen with him through the faith of the operation of God, who hath raised him from the dead." - Colossians 2:11-12 KJV

We cut off the sins of our flesh when we repent and are baptized in Jesus name.

"Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost." - Acts 2:38 KJV

*Chart from Search for Truth Bible Study