For those of us who employ some of the more esoteric methods of astrology, such as the sabian symbols and arabic parts, a minute changes A LOT. It not only changes the specific degree of the axis points, but each of the arabic parts as well. And when you interperet them through the sabian symbols, one degree completely changes the precept and inherent meaning of that activation point. The real steak and potatoes of the chart.
It should help to look up the sabian symbol for each of the possible ascending degrees, and see which one most fits or clicks as to who you are in this incarnation.
The sabian symbols can be read, as interpereted by Dane Rudhyar, here. Rudhyars summations are authentic and accurate. The real deal. (the holy grail of astrology, imho.)
For the degree of 29.xx, read the thirtieth degree of corresponding sign. For 00.xx degrees, read the first degree.
http://www.mindfire.ca/An%20Astrological%20Mandala/An%20Astrological%20Mandala%20-%20Contents.htm
The correct symbol should resonate with you on a personal level.
And remember, astrology is fluid, so a point close to the cusp will have some influence from both precepts, but likely one over the other.