Bluetooth Low Energy (BLE) is a popular technology within the Internet of Things. It allows low-power, star networks to be set up between a BLE gateway and multiple, power-constrained BLE devices. However, these networks tend to be static, not supporting BLE devices that can freely move around in an environment of multiple interconnected BLE gateways and perform handovers whenever necessary. This work proposes two alternative network architectures for mobile BLE peripherals. One leverages on IPv6 over BLE, whereas the other combines default BLE mechanisms with an additional custom controller. On top, we study in detail the handover mechanism that must be present in both architectures and compare the performance of both a passive and active handover approach. The passive handover approach can be set up without any extra implementation, but an active handover approach offers more proactive handover decisions and can provide a much lower handover latency. All proposed solutions have been implemented and validated on real hardware, showing the feasibility of having future infrastructures with support for mobile BLE devices.