Γεια σου, Άννα! Εννοείς, 'ψάχνω', 'αναζητώ' και όχι 'ζητώ' (to ask for) και 'γυρεύω' (the most poetic of the three, nowadays used in a more colloquial but at the same time emphatic way even among the younger generation: "Βρε, βρε το Μαράκι... Τί γυρεύρεις στα μέρη μας, πουλάκι μου;;; Καιρό έχουμε να σε δούμε"....). Remember that in Greek, when referring to a verb, we tend to use the first person in the present tense. Now, down to your question: yes, there are instances when you could use any of the three as well as moments/sentences in which only one of them is appropriate. For example: "Ζητώ/Ψάχνω/Γυρεύω να μάθω τί απέγινε ο φίλος των παιδικών μου χρόνων" & "Αναζητώ/Ψάχνω/Γυρεύω την αλήθεια" more or less mean the same thing and anyone would understand your point, no matter what the verb you'd use is. But, in cases such as: "Οι ρακοσυλλέκτες ψάχνουν στα σκουπίδια" cannot take a different verb (at least none of the other two mentioned above). "Ήρθε στο γραφείο μου ζητώντας πληροφορίες". "Γύρευε λούσα και την πάτησε" (OK! This is deep waters but never mind, it's interesting. Usually, this kind of saying goes for women and it means "she wanted the high life but was left with nothing"). I hope I helped and will be at your disposal for more queries-help. Λήδα