I would send a thank you after each stage. If possible, send them to the interviewer (s), but they may all be to the same person (recruiter or hiring manager). However, I would make them feel different (as opposed to the same two liner after each).
Thank you for taking the time to speak with me this afternoon and assess my fit for POSITION at COMPANY. Based on your explanation of the role, I believe EXPERIENCE could greatly assist COMPANY.
Please pass along my gratitude to HIRING MANAGER for providing valuable insight into POSITION. I look forward to meeting the team and discussing how EXPERIENCE can help PROBLEM.
I greatly enjoyed meeting TEAM MEMBERS this morning. I know they are busy and appreciate their time. I believe I would be a valuable addition to the TEAM. I look forward to continued discussion about joining COMPANY.