A set of three LADCP/CTD surveys covering the area of exchange between the Gulf of Mexico and Caribbean Sea is used to estimate the interchange and variability. The objectively mapped fields of velocity show, in a total of eight crossings, values of net inflow from 36 to 20 Sv (Sv=10^6 m^3/s). The transports into the Caribbean fluctuate from 6 to 16 Sv. The same maps added to those of density are modified conserving linear potential vorticity to render the geostrophicaly balanced fields. The natural boundary conditions for the inversion of the measured potential vorticity (as well as the conservation law itself) arise as a result of minimizing the internal waves energy (IWE) of linearized dynamics. The IEW is typically 2% of the total and equally balanced in kinetic and potential. In agreement with such low IEW there is no significant change in transports between those derived directly from the measurements and the geostrophic estimates. The mean geostrophic flow map shows the core of the Yucatan Current as the most intense feature with slow flows throughout the rest of the area. One region of outflow is underneath the Yucatan Current over the bottom from 500 to 1500 m deep on the Yucatan Slope. Another mean outflow occurs at the same depth range on the eastern side of the section, not against the Cuban Slope, and over a region of rough topography. The first EOF of the deviations from such mean has 45% of the variance with large values on the western edge of the Yucatan Current and a zero crossing dividing the western and eastern sides of the section. There is no indication of significant deep outflow over the sill in the mean or fluctuations.