Please explain what are the rules to join the different qira'a ( Hafs, qaloon, warsh etc) when reading on stage in public.
Wa alaikum assalaam wa rahmatullahi wa barakatuh,
One would be reading for demonstration purposes most likely in this case; to demonstrate the different qira'aat or give those present a 'taste" of the different qira'aat, to whet the Muslims interest in learning the different qira'aat.
This could be done in a number of ways. The first two ways are prescribed as allowed ways when getting an ijaazah in the qira'aat by the jam3 way. The third way is just for demonstration as far as we know.
1) Read each section (phrase or sentence until a stop sign), then go back from the end forward changing that which can be changed within the integrity of what was read already, moving forward towards the beginning of the section, changing the qir'ah closest to the "top" (the top being Naf'i) within the phrase integrity of each qira'ah.
The complete Qur'an read this way can be found at the bottom of the page at this link: http://www.taiser.net/quran.php
2) Read until a word with a rule which is different among the different qira'aat or a special word occurs, change the word for all those who change it, again in order from the "top" (Nafi'), then go on to the next word in the section, proceeding through until the end of the section or aayah.
3) Read a complete phrase, section, or aayah one way in one qira'ah or raawee, then read it again another way changing what needs to be changed, then on to the next qira'ah etc.
And Allah knows best.