っちゃあ is totally convertible to といえば, except that っちゃあ sounds very chatty and rough while といえば can be used in formal expressions. You can say 忙しいといえば忙しいけど, and it conveys the same meaning.
As for the word form, actually there are other forms like っていやあ and ってやあ. They phonetically seem to fall between といえば and っちゃあ, making the presumable process of sound change traceable like this:
- といえば /toieba/ -- original form.
- っていえば /Qteieba/ -- colloquial って instead of formal と
- っていやあ /QteiyaH/ -- b drops and ea collapses into yaH (keeping 2 moras)
- ってやあ /QteyaH/ -- i dissipates between e and y, because ofdue to its phonetical similarity to them.
- っちゃあ /QcyaH/ -- e drops and impossible *ty automatically turns cy
Plus, there is even more shortend form:
- っちゃ /Qcya/
All these six forms are possible, though #4 is rather rare.
By the way there are also forms like ってえば and ってば, which seem to be another line of sound change: Qteieba → QteHba → Qteba.