Recommendations for a good (rigorous) text to study Computational Complexity. I look for a good text to learn basics of computational complexity. 

I've read some parts of the first two chapters of "Computational Complexity: A Modern Approach" by Boaz Barak and Sanjeev Arora, it's readable and gives the big picture but I find it  not to be rigorious enough for me. I'm a mathematics student so I want a more rigorous treatment of the subject. So, the text I look for should:- 

1- Define Turing machines formally and prove the basic results in a formal way not using  handy-waving arguments. For example, Boaz treatment of Turing machines is not rigorous and so I'd love to see more precise treatment of that. 

2- Give proofs that are rigorous enough like those I read in mathematics texts and are not just "overviews".

What are your recommendations? What is the texts that satisfies my needs as close as possible?
Following are my recommendations:


Introduction to Theory of Computation by Michael Sipser. It is an introductory book. Although proofs are complete and not hand waving, but not much maths is needed as a pre requisite. Although Turing machines are covered nicely.
Complexity and cryptography by Talbolt and Welsh. In this book little math background is required. Turing machines is not covered in much details. But the book gives proofs for almost all theorem's it introduces. 
From my experience ( as I am a beginner myself ) Sanjeev Arora and Boaz Barak is the most concise with covering advanced topics like quantum computation etc. Although I think you should have a back ground in probability, number theory to read the part I of the book intended to be for undergraduates, as the book leaves some proofs upto the readers. Again for number theory the book I find readable as ( as there is no pre requisite ) :
Number theory by Willian Stein.