According to the Buddhism, "Next Birth" is not the person who lives in this birth. In the next birth, there is a person determined by the previous Karma
.
For certain concepts to be describe in particular in anicca
it is needed to believe reincarnation.
All of what we are ends with this birth. Only goodness and evil are taken to the next birth. So there is need to believe it for this reason.
For instance, If we are having good wealth and satisfaction through all the ways, we may think likelife is so happy and funny. But it is due to the meritorial deeds you have done in your past births. The effects of those good merits will end in one day. At the end of this birth or in future births. No one will be a good person all over his
Sansara
. So one day comes where you have to encounter sadness.