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:

1. といえば /toieba/ -- original form.
2. っていえば /Qteieba/ -- colloquial **って** instead of formal **と** 
3. っていやあ /QteiyaH/ -- **b** drops and **ea** collapses into **yaH** (keeping 2 moras)
4. ってやあ /QteyaH/ -- **i** dissipates between **e** and **y**, because of its phonetical similarity to them.
5. っちゃあ /QcyaH/ -- **e** drops and impossible ***ty** automatically turns **cy**

All five 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.