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12.6v is resting voltage. 12.9v is the minimum to get the battery to take a charge (2.15v/cell). 13.8v is fully charged/float voltage. 14.4v is cyclic/bulk charging voltage to balance the cells, and won't harm anything if it is switched over to float voltage once the battery is charged...chargers usually switch over from 14.4v at the end of bulk phase (80% charge) to 13.8v. Charging the battery over 14.4v will cause gassing, where the water in the electrolyte converts to hydrogen and oxygen. These voltages are for a battery at room temperature, and go up the colder the temperature and down the higher the temperature.
12.9v is probably as high as a 1-amp (peak) charge coming from the solar panel or a small charger can make the battery voltage rise. Or you have an inaccurate meter.
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