Bearss lime (also known as Tahitian lime or Persian lime) is one of the most common lime varieties grown in Arizona. It's seedless, vigorous, and grows dark green fruit that ripen to yellow.
I bought mine at Summerwinds Nursery and planted it in the spring of 2014. It bloomed in 2015 and had some fruit, though they all dropped. This year I finally have my first harvest. It's planted in the hottest spot of my yard (west-facing with full sun) along with grapefruit and a blood orange, so I provided some shade protection the first year.