I just finished the first three chapters from the book Calculus on Manifolds by Spivak. As you should know, a lot of obstacles arise from the chapter 4, "Integration on Chains". For example, missed important steps, erratas, bad notation, etc. I really want to read the theory and do the exercise from that book in a detailed way, but the purpose of this post is asking for a "little" help in reading it.
Can you suggest me some additional sources for filling those missing steps, erratas, etc. mentioned before? If it is possible, it would be great if the bibliography that you suggest contains some examples, as an antidote for the abstraction from Spivak.
I know that there exists some excellent books that would be helpful; for example, Munkres's Analysis on Manifolds, Ilka Agricola's Global Analysis, Tu's Introduction to Manifolds, and maybe some others. Do you think that those books are enough to deal with the theory from Spivak? Or do you know other sources (lecture notes, videos, etc)?
Any other advice would be well recieved. Thanks in advance! :)