You can definitely transition without cutting your hair. Try searching YouTube for videos on transitioning without doing the Big Chop (BC.) That's where I got most of my information.
The key to it is deep conditioning once a week, protective styling, and being careful of the line of demarcation (that's the point where your relaxed hair meets your natural hair, it's a lot more sensitive.) From what I can tell, working with your hair only when it is wet is key to being careful of that line. Never comb/brush your hair while it is dry. Use lots of moisture and seal your hair with oils (olive oil, coconut oil, castor oil.)
I hope this helps!