Line Interactive (or Active Stand By) technology is a recent development made possible by the appearance of microprocessors. The UPS is fully controlled by a microprocessor which monitors the quality of the mains power supply and reacts to any variations. This is what makes the UPS «Active» or «Interactive». Eaton Evolution and Evolution S range can supply the load correctly from input voltages varying between:

Voltage thresholds configuration on Evolution
As for the operating diagram, properly speaking, it is the same as on an Off-line (or Standby) device: in other words, in normal mode, the PC is supplied directly by the mains power supply, without any form of power conversion. In general, the current is filtered in order to attenuate the most frequent forms of disturbance.
In the event of a power problem, the UPS transfers the load to the batteries to supply stabilised power. It is increasingly frequent to add a voltage compensation circuit, called a «booster», that is enabled in the event of prolonged voltage drops. The benefits and trade-offs are explained below.
Some UPS manufacturers claim that this configuration can compete with an On-line configuration, because the DC/AC output converter is connected to the output at all times, as is the case with an On-line UPS. This argument is misleading and does not stand up to examination. The fact that the converter is connected does not necessarily mean that it is supplying power. In normal mode, its input is not connected to its power source, in other words the battery. Quite simply, on these products the switching relay is placed before the converter and not after it. In no way does this exclude the 4 ms transfer time, that is typical of conventional Off-line devices.