Hebrews 7 - Melchizedek is likened to Christ, verse 3. He received tithes from Abraham which means that the priests from the tribe of Levi also "paid tithes" through Abraham, verse 9. This shows that Christ's priesthood was greater than Aaron's and was able to give a "better covenant" than Levi, verses 11-22. Christ could save completely all of those who come to God through Him.
Hebrews 8 - The Aaronic priesthood was a type of Christ's ultimate ministry. Christ offered better promises through the "better covenant" He gave, verse 6, and made the first covenant "obsolete" verse 13.
Hebrews 9 - The Old Testament priest had to offer sacrifices for his own sins as well as for the people's sins, verse 7. But Christ only had to offer for the sins of the world once and could give "eternal redemption", verse 12. He did this not in an earthly temple, but "into heaven itself, now to appear in the presence of God for us" verse 24.
Hebrews 10 - Verse 4 makes clear that "it is not possible that the blood of bulls and goats could take away sins." But Christ's body was "sanctified" verse 10, and He could offer "one sacrifice for sins forever" and then He "sat down at the right hand of God", verse 12, thus showing His complete work for us. Because Christ shed His blood for our sins, we "have boldness to enter the Holiest by" that blood, verse 19. Believers are encouraged to stimulate one another to do good and they are also taught to assemble together for edification, verses 24,25.