The phrase "saw how it flies" can be replaced with a variety of synonyms depending on context and intended meaning. For example, one might say "observed its flight pattern" to convey a more scientific approach, or "marveled at its soaring" to emphasize awe or admiration. Other options include "witnessed its aerial acrobatics," "perceived its graceful flight," or "noticed how it glided through the air." The choice of synonym can impact the tone of the sentence, from analytical to poetic, and can help to convey a specific emotion or impression of the subject in question.