There is one verse in the Bible that refers to the third heaven: 2 Corinthians 12:2. Paul relates that he was taken up to the third heaven, which refers to the place where God resides. The first heaven is the atmosphere around the earth, the second refers to the domain of the stars. For a detailed explanation of this bible verse, please read the article ‘What is the third heaven?’
If you take ‘different levels of heaven’ to mean that there are different levels of blessedness, there is no reference to that in the Scriptures. But the Bible does talk about different rewards. Even though your salvation does not depend on your deeds but on faith in Christ alone, there are still various rewards and crowns. God promises the crown of life to those who are faithful and continue to love Him despite trials and tribulations (James 1:12; Revelation 2:10).
To those who are faithful leaders of the flock (a church), God promises a crown of glory (1 Peter 5:2-4). Paul exhorts his readers to run for an imperishable wreath; to be disciplined in the walk with the Lord and in preaching the Gospel (1 Corinthians 9:24,25). In another place, Paul talks of the crown of righteousness, which the Lord will give to all those who ‘have loved His (Jesus’) appearing’ (2 Timothy 4:8). Various bible verses mention rewards (for example: Matthew 5:12; 1 Corinthians 3:12-14).
The Lord values what we do
Maybe the idea of rewards seems strange to you. When you have always been taught that salvation is through the work of Christ Jesus alone, you might start thinking that works do not matter. Apparently, they do. Any child who is promised a reward for good work, will do his or her best more than when no such reward is mentioned. Likewise, God promises rewards to those who stand up under trials. Those who long for Jesus to return and who bring the Gospel untiringly. And those who lead others in the truth. The Lord values what we do! When Jesus returns, He will ‘repay each person according to what he has done’ (Matthew 16:27). Even the Lord Jesus fixed His eyes on the reward, the joy set before Him, for which he endured the cross. (Hebrews 12:1,2). The author of Hebrews exhorts us to be like Jesus and run the race. Let us be diligent and be faithful to the One who has always been faithful to us.