What's the difference between convalescence, recuperation, and recovery?
Convalescence is the period or process of becoming healthy and well again after an illness or operation.
⇒ Also thanks to Lucy and Guthrie Scott for inviting me to stay with them during my convalescence.

When you recuperate, you recover your health or strength after you have been ill or injured.
recuperation
⇒ Leonard was very pleased with his powers of recuperation.

If a sick person makes a recovery, he or she becomes well again.
⇒ He made a remarkable recovery from a shin injury.

http://www.collinsdictionary.com/dictionary/american-cobuild-learners

Are 'convalescence', 'recuperation, and 'recovery interchangeable' meaningly in the three sentences? If not, is there some difference between 'convalescence', 'recuperation', and 'recovery'?

Question

What's the difference between convalescence, recuperation, and recovery?
Convalescence is the period or process of becoming healthy and well again after an illness or operation.   
⇒ Also thanks to Lucy and Guthrie Scott for inviting me to stay with them during my convalescence.

When you recuperate, you recover your health or strength after you have been ill or injured.  
recuperation  
 ⇒ Leonard was very pleased with his powers of recuperation.

If a sick person makes a recovery, he or she becomes well again.   
⇒ He made a remarkable recovery from a shin injury.

http://www.collinsdictionary.com/dictionary/american-cobuild-learners

Are 'convalescence', 'recuperation, and 'recovery interchangeable' meaningly in the three sentences? If not, is there some difference between 'convalescence', 'recuperation', and 'recovery'?

Answer

First you 'recover' from your illness. That's recovery. Then you have a period where you are not ill any more, but you need some time to rest and get your strength back - this is recuperation or convalescence. I'm not sure of the exact difference between the two, but convalescence sounds more old-fashioned (old ladies in with blankets tucked around them) , whereas recuperation feels a bit more modern and medical (might include eg physiotherapy).