Two vertical turbulent round jets are used to levitate a spherical particle. First, a symmetric configuration is investigated with the two jets of equal flow rates. A structure reminiscent of a pitchfork bifurcation is reported and characterized between a double trap configuration for low flow rates and a single trap regime at larger flow rates. A second configuration is then studied with the flow rates that differ between the left and the right jets. In this case, a preferential transition towards the jet of higher flow rate is reported and quantified. A model is presented predicting the force field for the symmetric and the asymmetric configurations. The model is compared to the force field measurements realized with a particle on a flexible cantilever. Finally, a particle dynamics simulation is proposed to analyze in more details the transition for the levitation in the symmetric and the asymmetric configurations.