Holographic acoustical tweezers based on Archimedes-Fermat spiraling interdigitated transducers (SIDTs) are a versatile tool for the selective manipulation of microparticles [Baudoin et al., Sci. Adv. 5, eaav1967 (2019)] and cells [Baudoin et al., Nat. Commun., 11, 4244 (2020)] in a standard microfluidic environment. These binary active holograms produce some focused helical wave, with the ability to trap particles at the vortex core. Yet, all the studies conducted with SIDTs have so far been restricted to two-dimensional (2D) manipulation only. Here we show through a theoretical study that (i) a 3D radiation trap for microparticles and cells can be obtained with spiraling tweezers with sufficiently large aperture and that (ii) the particles can be displaced axially by simply tuning the driving frequency, without any motion of the transducer. This work opens perspectives for 3D cells and microparticles manipulation with single-beam acoustical tweezers.